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  </channel><item rdf:about="https://inria.hal.science/hal-05593313v1">
    <title>Computing hard-to-round cases of sin, cos, tan in double precision - Inria - Institut national de recherche en sciences et technologies du numérique</title>
    <dc:date>2026-05-24T12:22:36+00:00</dc:date>
    <link>https://inria.hal.science/hal-05593313v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper describes an exhaustive search algorithm to find the hardest-to-round cases of trigonometric functions (sin, cos, tan) in double precision (binary64). This algorithm reuses a clever reduction from the literature, but instead of using a sublinear search, it uses a brute force linear search. This algorithm was implemented using multi-threading and SIMD, and a full set of hard-to-round cases for the binary64 trigonometric functions was computed. As a consequence, the Table Maker's Dilemma is now fully solved for the most common univariate binary64 functions.

]]></description>
<dc:subject>numerical-methods computational-complexity algorithms rather-interesting special-cases to-write-about to-simulate approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6249741238f1/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
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<item rdf:about="https://arxiv.org/abs/2407.03357">
    <title>[2407.03357] Elementary Formulas for Greatest Common Divisors and Semiprime Factors</title>
    <dc:date>2026-05-24T11:08:57+00:00</dc:date>
    <link>https://arxiv.org/abs/2407.03357</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We conjecture new elementary formulas for computing the greatest common divisor (GCD) of two integers, alongside an elementary formula for extracting the prime factors of semiprimes. These formulas are of fixed-length and require only the basic arithmetic operations of: addition, subtraction, multiplication, division with remainder, and exponentiation. Our GCD formulas result from simplifying a formula of Mazzanti and are derived using Kronecker substitution techniques from our earlier research. By applying these GCD formulas together with our recent discovery of an arithmetic expression for n‾√, we are able to derive explicit elementary formulas for the prime factors of a semiprime n=pq.
]]></description>
<dc:subject>algorithms numerical-methods computational-complexity rather-interesting performance-measure consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:99ab92c256bf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
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<item rdf:about="https://dl.acm.org/doi/full/10.1145/3674634">
    <title>The Long Way to Deforestation: A Type Inference and Elaboration Technique for Removing Intermediate Data Structures | Proceedings of the ACM on Programming Languages</title>
    <dc:date>2026-02-25T22:06:02+00:00</dc:date>
    <link>https://dl.acm.org/doi/full/10.1145/3674634</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Deforestation is a compiler optimization that removes intermediate data structure allocations from functional programs to improve their efficiency. This is an old idea, but previous approaches have proved limited or impractical — they either only worked on compositions of predefined combinators (shortcut fusion), or involved the aggressive unfolding of recursive definitions until a depth limit was reached or a reoccurring pattern was found to tie the recursive knot, resulting in impractical algorithmic complexity and large amounts of code duplication. We present Lumberhack, a general-purpose deforestation approach for purely functional call-by-need and call-by-value programs. Lumberhack uses subtype inference to reason about data structure production and consumption and uses an elaboration pass to fuse the corresponding recursive definitions. It fuses large classes of mutually recursive definitions while avoiding much of the unproductive (and sometimes counter-productive) code duplication inherent in previous approaches. We prove the soundness of Lumberhack using step-indexed logical relations and experimentally demonstrate significant speedups in the standard nofib benchmark suite. We manually adapted nofib programs to call-by-value semantics and compiled them using the OCaml compiler. The average speedup over the 38 benchmarked programs is 
8.2
%
 while the average code size increases by just about 
1
.
79
x
. In particular, 19 programs see their performance mostly unchanged, 17 programs improve significantly (by an average speedup of 
16.6
%
), and only two programs visibly worsen (by an average slowdown of 
1.8
%
). As a point of comparison, we measured that the well-proven but semi-manual list fusion technique of the Glasgow Haskell Compiler (GHC), which only works for call-by-need programs, had an average speedup of 
6.5
%
. Our technique is still in its infancy and misses some deforestation opportunities. We are confident that further refinements will yield greater performance improvements in the future.
]]></description>
<dc:subject>computer-science symbolic-analysis formal-languages functional-programming to-understand computational-complexity efficiency consider:Push</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e124ca6a05b6/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2504.03460">
    <title>[2504.03460] Verified Program Extraction in Number Theory: The Fundamental Theorem of Arithmetic and Relatives</title>
    <dc:date>2026-02-20T14:02:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2504.03460</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include Bézout's identity, the fundamental theorem of arithmetic, and Fermat's factorisation method. All definitions and theorems are fully formalised in the proof assistant Minlog, laying the foundation for a comprehensive formal framework for number theory within Minlog.
While formalisation guarantees correctness, the primary emphasis is on the computational content of proofs. Leveraging Minlog's built-in program extraction, we obtain executable terms and export them as Haskell code.
The efficiency of the extracted programs plays a central role. We show how performance considerations influence even the original formulation of theorems and proofs. In particular, we compare formalisations based on binary encodings of natural numbers with those using the traditional unary (successor-based) representation.
We present several core proofs in detail and reflect on the challenges that arise from formalisation in contrast to informal reasoning. The complete formalisation is available online and linked throughout. Minlog's tactic scripts are designed to follow the structure of natural-language proofs, allowing each derivation step to be traced precisely and thereby bridging the gap between formal and classical mathematical reasoning.
]]></description>
<dc:subject>number-theory logic-programming rather-interesting theorem-proving to-understand computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6bfd6da31ac7/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:theorem-proving"/>
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<item rdf:about="https://arxiv.org/abs/1109.5635">
    <title>[1109.5635] Approximating Edit Distance in Near-Linear Time</title>
    <dc:date>2025-12-31T18:17:15+00:00</dc:date>
    <link>https://arxiv.org/abs/1109.5635</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show how to compute the edit distance between two strings of length n up to a factor of 2^{Õ(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time, improving on the state-of-the-art n^(1/3+o(1)) approximation. Previously, approximation of 2^{Õ(sqrt(log n))} was known only for embedding edit distance into l_1, and it is not known if that embedding can be computed in less than quadratic time.
]]></description>
<dc:subject>strings edit-distance algorithms computational-complexity rather-interesting to-understand follow-cites</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7479f24f2b7a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
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<item rdf:about="https://arxiv.org/abs/2005.07678">
    <title>[2005.07678] Edit Distance in Near-Linear Time: it's a Constant Factor</title>
    <dc:date>2025-12-31T17:56:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.07678</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present an algorithm for approximating the edit distance between two strings of length n in time n1+ε up to a constant factor, for any ε>0. Our result completes a research direction set forth in the recent breakthrough paper [Chakraborty-Das-Goldenberg-Koucky-Saks, FOCS'18], which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time. The recent results of [Koucky-Saks, STOC'20] and [Brakensiek-Rubinstein, STOC'20] have shown near-linear time algorithms that obtain an additive approximation, near-linear in n (equivalently, constant-factor approximation when the edit distance value is close to n). In contrast, our algorithm obtains a constant-factor approximation in near-linear time for any input strings.
In contrast to prior algorithms, which are mostly recursing over smaller substrings, our algorithm gradually smoothes out the local contribution to the edit distance over progressively larger substrings. To accomplish this, we iteratively construct a distance oracle data structure for the metric of edit distance on all substrings of input strings, of length niε for i=0,1,…,1/ε. The distance oracle approximates the edit distance over these substrings in a certain average sense, just enough to estimate the overall edit distance.
]]></description>
<dc:subject>strings computational-complexity algorithms rather-interesting approximation to-write-about to-implement consider:Push-code</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:71df08420968/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:Push-code"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2112.12678">
    <title>[2112.12678] Dynamic Suffix Array with Sub-linear update time and Poly-logarithmic Lookup Time</title>
    <dc:date>2025-08-17T12:19:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2112.12678</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Suffix Array SAS[1…n] of an n-length string S is a lexicographically sorted array of the suffixes of S. The suffix array is one of the most well known and widely used data structures in string algorithms. We present a data structure for maintaining a representation of the suffix array of a dynamic string which undergoes symbol substitutions, deletions, and insertions.
For every string manipulation, our data structure can be updated in O(n23) time (ignoring multiplicative polylogarithmic factors) with n being the current length of the string. For an input query i∈[1…n], our data structure reports SAS[i] in O(log5(n)) time.
We also present a faster data structure, with O(n‾√) update time (ignoring multiplicative polylogarithmic factors), for maintaining the Inverted Suffix Array of a dynamic string undergoing symbol substitutions updates. For an input query i∈[1…n], our data structure reports the i'th entry in the inverted suffix array in O(log4(n)) time.
Our data structures can be used to obtain sub-linear dynamic algorithms for several classical string problems for which efficient dynamic solutions were not previously known.]]></description>
<dc:subject>data-structures symbolic-dynamics strings computational-complexity rather-interesting to-understand this-might-be-just-the-thing ReQ</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b2621692edf2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symbolic-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ReQ"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.15542">
    <title>[2209.15542] The worst approximable rational numbers</title>
    <dc:date>2025-08-11T13:51:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.15542</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We classify and enumerate all rational numbers with approximation constant at least 13 using hyperbolic geometry. Rational numbers correspond to geodesics in the modular torus with both ends in the cusp, and the approximation constant measures how far they stay out of the cusp neighborhood in between. Compared to the original approach, the geometric point of view eliminates the need to discuss the intricate symbolic dynamics of continued fraction representations, and it clarifies the distinction between the two types of worst approximable rationals: (1) There is a plane forest of Markov fractions whose denominators are Markov numbers. They correspond to simple geodesics in the modular torus with both ends in the cusp. (2) For each Markov fraction, there are two infinite sequences of companions, which correspond to non-simple geodesics with both ends in the cusp that do not intersect a pair of disjoint simple geodesics, one with both ends in the cusp and one closed.
]]></description>
<dc:subject>number-theory approximation rational-numbers rather-interesting looking-to-see computational-complexity to-write-about to-simulate representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:73b9846f5700/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rational-numbers"/>
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<item rdf:about="https://dl.acm.org/doi/abs/10.1145/3715739">
    <title>QSF: Multi-objective Optimization Based Efficient Solving for Floating-Point Constraints | Proceedings of the ACM on Software Engineering</title>
    <dc:date>2025-06-24T14:55:59+00:00</dc:date>
    <link>https://dl.acm.org/doi/abs/10.1145/3715739</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Floating-point constraint solving is challenging due to the complex representation and non-linear computations. Search-based constraint solving provides an effective method for solving floating-point constraints. In this paper, we propose QSF to improve the efficiency of search-based solving for floating-point constraints. The key idea of QSF is to model the floating-point constraint solving problem as a multi-objective optimization problem. Specifically, QSF considers both the number of unsatisfied constraints and the sum of the violation degrees of unsatisfied constraints as the objectives for search-based optimization. Besides, we propose a new evolutionary algorithm in which the mutation operators are specially designed for floating-point numbers, aiming to solve the multi-objective problem more efficiently. We have implemented QSF and conducted extensive experiments on both the SMT-COMP benchmark and the benchmark from real-world floating-point programs. The results demonstrate that compared to SOTA floating-point solvers, QSF achieved an average speedup of 15.72X under a 60-second timeout and an impressive 87.48X under a 600-second timeout on the first benchmark. Similarly, on the second benchmark, QSF delivered an average speedup of 22.44X and 29.23X, respectively, under the two timeout configurations. Furthermore, QSF has also enhanced the performance of symbolic execution for floating-point programs.]]></description>
<dc:subject>numerical-methods multiobjective-optimization constraint-satisfaction computational-complexity rather-interesting operations-research to-write-about to-simulate consider:lexicase</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:52946ee4b76f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/doi/10.1073/pnas.0710743106">
    <title>Efficient computation of optimal actions | PNAS</title>
    <dc:date>2025-05-27T22:44:00+00:00</dc:date>
    <link>https://www.pnas.org/doi/10.1073/pnas.0710743106</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress—as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.]]></description>
<dc:subject>machine-learning approximation algorithms rather-interesting computational-complexity to-understand mathematical-programming metaheuristics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d4e94025ab87/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.13103">
    <title>[2109.13103] Efficiently solving the thief orienteering problem with a max-min ant colony optimization approach</title>
    <dc:date>2024-11-16T14:50:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.13103</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We tackle the Thief Orienteering Problem (ThOP), an academic multi-component problem that combines two classical combinatorial problems, namely the Knapsack Problem and the Orienteering Problem. In the ThOP, a thief has a time limit to steal items that distributed in a given set of cities. While traveling, the thief collects items by storing them in their knapsack, which in turn reduces the travel speed. The thief has as the objective to maximize the total profit of the stolen items. In this article, we present an approach that combines swarm-intelligence with a randomized packing heuristic. Our solution approach outperforms existing works on almost all the 432 benchmarking instances, with significant improvements.
]]></description>
<dc:subject>multiobjective-optimization operations-research computational-complexity rather-interesting metaheuristics to-write-about consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:674b873506e1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.04320">
    <title>[2212.04320] A 65nm 8b-Activation 8b-Weight SRAM-Based Charge-Domain Computing-in-Memory Macro Using A Fully-Parallel Analog Adder Network and A Single-ADC Interface</title>
    <dc:date>2024-11-01T19:14:15+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.04320</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Performing data-intensive tasks in the von Neumann architecture is challenging to achieve both high performance and power efficiency due to the memory wall bottleneck. Computing-in-memory (CiM) is a promising mitigation approach by enabling parallel in-situ multiply-accumulate (MAC) operations within the memory with support from the peripheral interface and datapath. SRAM-based charge-domain CiM (CD-CiM) has shown its potential of enhanced power efficiency and computing accuracy. However, existing SRAM-based CD-CiM faces scaling challenges to meet the throughput requirement of high-performance multi-bit-quantization applications. This paper presents an SRAM-based high-throughput ReLU-optimized CD-CiM macro. It is capable of completing MAC and ReLU of two signed 8b vectors in one CiM cycle with only one A/D conversion. Along with non-linearity compensation for the analog computing and A/D conversion interfaces, this work achieves 51.2GOPS throughput and 10.3TOPS/W energy efficiency, while showing 88.6% accuracy in the CIFAR-10 dataset.
]]></description>
<dc:subject>algorithms computer-science architecture to-understand unconventional-computing acceleration computational-complexity consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c7c2b27eeb14/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:architecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unconventional-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:acceleration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://hal.science/hal-04710512v1">
    <title>The Harmonious Coloring Game - Archive ouverte HAL</title>
    <dc:date>2024-10-05T14:09:10+00:00</dc:date>
    <link>https://hal.science/hal-04710512v1</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A harmonious k-coloring of a graph G is a 2-distance proper k-coloring of its vertices such that each edge is uniquely identified by the colors of its endpoints. Here, we introduce its game version: the harmonious coloring game. In this two-player game, Alice and Bob alternately select an uncolored vertex and assigns to it a color in {1, . . . , k} with the constraint that, at every turn, the set of colored vertices induces a valid partial harmonious coloring. Alice wins if all vertices are colored; otherwise, Bob wins. The harmonious game chromatic number χ hg (G) is the minimum integer k such that Alice has a winning strategy with k colors. In this paper, we prove the PSPACE-hardness of three variants of this game. As a by-product, we prove that a variant introduced by Chen et al. in 1997 of the classical graph coloring game is PSPACE-hard. We also obtain lower and upper bounds for χ hg (G) in graph classes, such as paths, cycles, grids and forests of stars.

]]></description>
<dc:subject>graph-theory mathematical-recreations game-theory rather-interesting computational-complexity to-write-about to-simulate consider:looking-to-see consider:random-sampling consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0ecde86680b1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:game-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:random-sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2112.12197">
    <title>[2112.12197] Computable Model Discovery and High-Level-Programming Approximations to Algorithmic Complexity</title>
    <dc:date>2024-09-08T15:23:21+00:00</dc:date>
    <link>https://arxiv.org/abs/2112.12197</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however, significantly restricts a wider application of exhaustive methods. Here we present a proof of concept of an approach based on IMP, a high-level imperative programming language. Its main advantage is that conceptually complex computational routines are more succinctly expressed, unlike lower-level models such as Turing machines or cellular automata. We investigate if a more expressive higher-level programming language can be more efficient at generating approximations to algorithmic complexity of recursive functions, often of particular mathematical interest.
]]></description>
<dc:subject>algorithmic-information-theory AIT computational-complexity looking-to-see rather-interesting halting-problem enumeration combinatorics to-understand consider:FFX consider:not-worrying</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:872641e819d6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithmic-information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:AIT"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:halting-problem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:FFX"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:not-worrying"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2308.08868">
    <title>[2308.08868] Computing complexity measures of degenerate graphs</title>
    <dc:date>2024-04-01T11:33:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2308.08868</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that the VC-dimension of a graph can be computed in time nlogd+1dO(d), where d is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that see a specific subset of vertices inside of a (small) query set. The construction of this data structure takes time O(d2dn), afterwards queries can be computed efficiently using fast Möbius inversion.
This data structure turns out to be useful for a range of tasks, especially for finding bipartite patterns in degenerate graphs, and we outline an efficient algorithms for counting the number of times specific patterns occur in a graph. The largest factor in the running time of this algorithm is O(nc), where c is a parameter of the pattern we call its left covering number.
Concrete applications of this algorithm include counting the number of (non-induced) bicliques in linear time, the number of co-matchings in quadratic time, as well as a constant-factor approximation of the ladder index in linear time.
Finally, we supplement our theoretical results with several implementations and run experiments on more than 200 real-world datasets -- the largest of which has 8 million edges -- where we obtain interesting insights into the VC-dimension of real-world networks.
]]></description>
<dc:subject>computational-complexity graph-theory algorithms horse-races rather-interesting looking-to-see to-write-about consider:evolved consider:stress-testing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:368bb27f15be/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:evolved"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:stress-testing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.07524">
    <title>[2209.07524] $tilde{O}(n+mathrm{poly}(k))$-time Algorithm for Bounded Tree Edit Distance</title>
    <dc:date>2023-10-10T10:10:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.07524</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of dissimilarity between two (unweighted) rooted trees with node labels. Perhaps the most notable recent application of tree edit distance is in NoSQL big databases, such as MongoDB, where each row of the database is a JSON document represented as a labeled rooted tree, and finding dissimilarity between two rows is a basic operation. Until recently, the fastest algorithm for tree edit distance ran in cubic time (Demaine, Mozes, Rossman, Weimann; TALG'10); however, Mao (FOCS'21) broke the cubic barrier for the tree edit distance problem using fast matrix multiplication.
Given a parameter k as an upper bound on the distance, an O(n+k2)-time algorithm for edit distance has been known since the 1980s due to the works of Myers (Algorithmica'86) and Landau and Vishkin (JCSS'88). The existence of an Õ(n+poly(k))-time algorithm for tree edit distance has been posed as an open question, e.g., by Akmal and Jin (ICALP'21), who gave a state-of-the-art Õ(nk2)-time algorithm. In this paper, we answer this question positively.
]]></description>
<dc:subject>distance metrics edit-distance rather-interesting algorithms computational-complexity to-understand to-write-about consider:genetic-programming consider:structure-function</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:266589466b64/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:structure-function"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.09663">
    <title>[2205.09663] Collision Detection Accelerated: An Optimization Perspective</title>
    <dc:date>2023-09-30T12:37:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.09663</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Collision detection between two convex shapes is an essential feature of any physics engine or robot motion planner. It has often been tackled as a computational geometry problem, with the Gilbert, Johnson and Keerthi (GJK) algorithm being the most common approach today. In this work we leverage the fact that collision detection is fundamentally a convex optimization problem. In particular, we establish that the GJK algorithm is a specific sub-case of the well-established Frank-Wolfe (FW) algorithm in convex optimization. We introduce a new collision detection algorithm by adapting recent works linking Nesterov acceleration and Frank-Wolfe methods. We benchmark the proposed accelerated collision detection method on two datasets composed of strictly convex and non-strictly convex shapes. Our results show that our approach significantly reduces the number of iterations to solve collision detection problems compared to the state-of-the-art GJK algorithm, leading to up to two times faster computation times.
]]></description>
<dc:subject>numerical-methods computational-complexity computational-geometry algorithms rather-interesting nudge-targets consider:looking-to-see to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:28b76b883a7e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2210.02292">
    <title>[2210.02292] Double-Ended Palindromic Trees: A Linear-Time Data Structure and Its Applications</title>
    <dc:date>2023-09-09T13:40:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2210.02292</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The palindromic tree (a.k.a. eertree) is a linear-size data structure that provides access to all palindromic substrings of a string. In this paper, we propose a generalized version of eertree, called double-ended eertree, which supports linear-time online double-ended queue operations on the stored string. At the heart of our construction, is a class of substrings, called surfaces, of independent interest. Namely, surfaces are neither prefixes nor suffixes of any other palindromic substrings and characterize the link structure of all palindromic substrings in the eertree. 
As an application, we develop a framework for range queries involving palindromes on strings, including counting distinct palindromic substrings, and finding the longest palindromic substring, shortest unique palindromic substring and shortest absent palindrome of any substring. In particular, offline queries only use linear space. Apart from range queries, we enumerate palindromic rich strings with a given word in linear time on the length of the given word.
]]></description>
<dc:subject>strings palindromes algorithms computational-complexity data-structures rather-interesting to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fa87703719d4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:palindromes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://dl.acm.org/doi/10.1145/234535.234536">
    <title>Computing the discrepancy with applications to supersampling patterns | ACM Transactions on Graphics</title>
    <dc:date>2023-08-08T11:27:53+00:00</dc:date>
    <link>https://dl.acm.org/doi/10.1145/234535.234536</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy—how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.
]]></description>
<dc:subject>computational-geometry algorithms computational-complexity discrepancy numerical-methods monte-carlo to-write-about to-implement to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:607e399d731c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrepancy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:monte-carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-implement"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.09618">
    <title>[2207.09618] Dynamical system-based computational models for solving combinatorial optimization on hypergraphs</title>
    <dc:date>2023-07-30T16:19:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.09618</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping such dynamics to combinatorial optimization problems whose objective functions have quadratic degree (e.g., MaxCut); such problems can be represented and analyzed using graphs. However, the work on developing such models for problems that need objective functions with degree greater than two, and subsequently, entail the use of hypergraph data structures, is relatively sparse. In this work, we develop dynamical system-inspired computational models for several such problems. Specifically, we define the 'energy function' for hypergraph-based combinatorial problems ranging from Boolean SAT and its variants to integer factorization, and subsequently, define the resulting system dynamics. We also show that the design approach is applicable to optimization problems with quadratic degree, and use it develop a new dynamical system formulation for minimizing the Ising Hamiltonian. Our work not only expands on the scope of problems that can be directly mapped to, and solved using physics-inspired models, but also creates new opportunities to design high-performance accelerators for solving combinatorial optimization.
]]></description>
<dc:subject>optimization computational-complexity metaheuristics rather-interesting numerical-methods hypergraphs representation distributed-processing to-write-about</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f9687f995259/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:metaheuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.13202">
    <title>[2205.13202] More Recent Advances in (Hyper)Graph Partitioning</title>
    <dc:date>2023-04-12T13:06:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.13202</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic. In particular, the survey extends the previous survey by also covering hypergraph partitioning and streaming algorithms, and has an additional focus on parallel algorithms.
]]></description>
<dc:subject>hypergraphs graph-theory algorithms computational-complexity rather-interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aa408bec37d3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2109.08962">
    <title>[2109.08962] On integer partitions and continued fraction type algorithms</title>
    <dc:date>2023-02-07T13:01:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2109.08962</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show that the additive-slow-Farey version of the traditional continued fractions algorithm has a natural interpretation as a method for producing integer partitions of a positive number n into two smaller numbers, with multiplicity. We provide a complete description of how such integer partitions occur and of the conjugation for the corresponding Young shapes via the dynamics of the classical Farey tree. We use the dynamics of the Farey map to get a new formula for p(2,n), the number of ways for partitioning n into two smaller positive integers, with multiplicity. We then do the analogue using the additive-slow-Farey version of the Triangle map (a type of multi-dimensional continued fraction algorithm), giving us a method for producing integer partitions of a positive number n into three smaller numbers, with multiplicity. However different aspects of this generalisations remain unclear.
]]></description>
<dc:subject>number-theory enumeration continued-fractions rather-interesting to-understand representation approximation optimization computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2d5320455881/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:number-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:continued-fractions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2203.01794">
    <title>[2203.01794] Efficient Fréchet distance queries for segments</title>
    <dc:date>2023-01-01T13:09:52+00:00</dc:date>
    <link>https://arxiv.org/abs/2203.01794</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the problem of constructing a data structure that can store a two-dimensional polygonal curve P, such that for any query segment ab⎯⎯⎯⎯⎯⎯ one can efficiently compute the Fréchet distance between P and ab⎯⎯⎯⎯⎯⎯. First we present a data structure of size O(nlogn) that can compute the Fréchet distance between P and a horizontal query segment ab⎯⎯⎯⎯⎯⎯ in O(logn) time, where n is the number of vertices of P. In comparison to prior work, this significantly reduces the required space. We extend the type of queries allowed, as we allow a query to be a horizontal segment ab⎯⎯⎯⎯⎯⎯ together with two points s,t∈P (not necessarily vertices), and ask for the Fréchet distance between ab⎯⎯⎯⎯⎯⎯ and the curve of P in between s and t. Using O(nlog2n) storage, such queries take O(log3n) time, simplifying and significantly improving previous results. We then generalize our results to query segments of arbitrary orientation. We present an O(nk3+ε+n2) size data structure, where k∈[1..n] is a parameter the user can choose, and ε>0 is an arbitrarily small constant, such that given any segment ab⎯⎯⎯⎯⎯⎯ and two points s,t∈P we can compute the Fréchet distance between ab⎯⎯⎯⎯⎯⎯ and the curve of P in between s and t in O((n/k)log2n+log4n) time. This is the first result that allows efficient exact Fréchet distance queries for arbitrarily oriented segments. 
We also present two applications of our data structure: we show that we can compute a local δ-simplification (with respect to the Fréchet distance) of a polygonal curve in O(n5/2+ε) time, and that we can efficiently find a translation of an arbitrary query segment ab⎯⎯⎯⎯⎯⎯ that minimizes the Fréchet distance with respect to a subcurve of P.
]]></description>
<dc:subject>computational-geometry computational-complexity algorithms distance preprocessing approximation rather-interesting to-simulate to-write-about consider:oracles</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:5471ba660ae6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:preprocessing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:oracles"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1203.4667">
    <title>[1203.4667] Turing machines can be efficiently simulated by the General Purpose Analog Computer</title>
    <dc:date>2022-05-14T10:50:13+00:00</dc:date>
    <link>https://arxiv.org/abs/1203.4667</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis.
]]></description>
<dc:subject>analog-computing representation simulation computational-complexity to-understand nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:adde835968e4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:analog-computing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.01567">
    <title>[2102.01567] A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants</title>
    <dc:date>2022-03-29T15:46:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.01567</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper develops an unified framework to study finite-sample convergence guarantees of a large class of value-based asynchronous reinforcement learning (RL) algorithms. We do this by first reformulating the RL algorithms as \textit{Markovian Stochastic Approximation} (SA) algorithms to solve fixed-point equations. We then develop a Lyapunov analysis and derive mean-square error bounds on the convergence of the Markovian SA. Based on this result, we establish finite-sample mean-square convergence bounds for asynchronous RL algorithms such as Q-learning, n-step TD, TD(λ), and off-policy TD algorithms including V-trace. As a by-product, by analyzing the convergence bounds of n-step TD and TD(λ), we provide theoretical insights into the bias-variance trade-off, i.e., efficiency of bootstrapping in RL. This was first posed as an open problem in (Sutton, 1999).
]]></description>
<dc:subject>machine-learning horse-races resource-allocation rather-interesting computational-complexity to-write-about consider:lexicase consider:comparison-to-archiving</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6847dc3122f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:horse-races"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:resource-allocation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:comparison-to-archiving"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.07512">
    <title>[2105.07512] Substitutional Neural Image Compression</title>
    <dc:date>2022-03-17T10:52:01+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.07512</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We describe Substitutional Neural Image Compression (SNIC), a general approach for enhancing any neural image compression model, that requires no data or additional tuning of the trained model. It boosts compression performance toward a flexible distortion metric and enables bit-rate control using a single model instance. The key idea is to replace the image to be compressed with a substitutional one that outperforms the original one in a desired way. Finding such a substitute is inherently difficult for conventional codecs, yet surprisingly favorable for neural compression models thanks to their fully differentiable structures. With gradients of a particular loss backpropogated to the input, a desired substitute can be efficiently crafted iteratively. We demonstrate the effectiveness of SNIC, when combined with various neural compression models and target metrics, in improving compression quality and performing bit-rate control measured by rate-distortion curves. Empirical results of control precision and generation speed are also discussed.
]]></description>
<dc:subject>image-processing neural-networks generative-models approximation compression to-write-about to-visualize consider:performance-measures machine-learning computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e52739abcbfa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:compression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1709.02990">
    <title>[1709.02990] Large monochromatic components and long monochromatic cycles in random hypergraphs</title>
    <dc:date>2022-03-15T15:51:26+00:00</dc:date>
    <link>https://arxiv.org/abs/1709.02990</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We extend results of Gyárfás and Füredi on the largest monochromatic component in r-colored complete k-uniform hypergraphs to the setting of random hypergraphs. We also study long monochromatic loose cycles in r-colored random hypergraphs. In particular, we obtain a random analog of a result of Gyárfás, Sárközy, and Szemerédi on the longest monochromatic loose cycle in 2-colored complete k-uniform hypergraphs.
]]></description>
<dc:subject>hypergraphs graph-theory algorithms graph-coloring computational-complexity to-understand to-write-about to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c45ed0ef1df5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-coloring"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2001.04109">
    <title>[2001.04109] On fast multiplication of a matrix by its transpose</title>
    <dc:date>2022-02-28T13:59:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2001.04109</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions.Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite this http URL conclude, we show how to use our result in LDLT factorization.
]]></description>
<dc:subject>matrices algorithms numerical-methods computational-complexity rather-interesting to-write-about to-visualize consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:14bb5e1045e9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2010.15770">
    <title>[2010.15770] Recursive Random Contraction Revisited</title>
    <dc:date>2022-02-17T11:10:28+00:00</dc:date>
    <link>https://arxiv.org/abs/2010.15770</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this note, we revisit the recursive random contraction algorithm of Karger and Stein for finding a minimum cut in a graph. Our revisit is occasioned by a paper of Fox, Panigrahi, and Zhang which gives an extension of the Karger-Stein algorithm to minimum cuts and minimum k-cuts in hypergraphs. When specialized to the case of graphs, the algorithm is somewhat different than the original Karger-Stein algorithm. We show that the analysis becomes particularly clean in this case: we can prove that the probability that a fixed minimum cut in an n node graph is returned by the algorithm is bounded below by 1/(2Hn−2), where Hn is the nth harmonic number. We also consider other similar variants of the algorithm, and show that no such algorithm can achieve an asymptotically better probability of finding a fixed minimum cut.
]]></description>
<dc:subject>graph-theory algorithms hypergraphs computational-complexity to-simulate to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:56b524ee82bd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.02329">
    <title>[2005.02329] Many visits TSP revisited</title>
    <dc:date>2022-02-09T13:13:14+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.02329</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the Many Visits TSP problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 2019, TALG 2020] and runs in time and space ∗(5n). They also show a polynomial space algorithm running in time ∗(16n+o(n)). 
In this work, we show three main results: (i) A randomized polynomial space algorithm in time ∗(2nD), where D is the maximum distance between two cities. By using standard methods, this results in (1+ϵ)-approximation in time ∗(2nϵ−1). Improving the constant 2 in these results would be a major breakthrough, as it would result in improving the ∗(2n)-time algorithm for Directed Hamiltonian Cycle, which is a 50 years old open problem. (ii) A tight analysis of Berger et al.'s exponential space algorithm, resulting in ∗(4n) running time bound. (iii) A new polynomial space algorithm, running in time (7.88n).
]]></description>
<dc:subject>TSP optimization computational-complexity algorithms rather-interesting to-write-about consider:differences-in-behavior consider:sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:066a49583f08/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:TSP"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:differences-in-behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2010.11448">
    <title>[2010.11448] Parallel Algorithms and Heuristics for Efficient Computation of High-Order Line Graphs of Hypergraphs</title>
    <dc:date>2022-02-01T12:14:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2010.11448</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common "neighbor". However, minimal commonality sometimes discards the "strength" of connections and interactions among groups. To this end, considering the "width" of a connection, referred to as the s-overlap of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, s-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the s-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute s-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the s-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than 10×) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large s value).
]]></description>
<dc:subject>hypergraphs graph-theory algorithms rather-interesting computational-complexity consider:the-thing-rather-than-the-method</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b4e033a7becf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:the-thing-rather-than-the-method"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2108.08613">
    <title>[2108.08613] A Conditional Lower Bound for Episode Matching</title>
    <dc:date>2022-01-29T14:04:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2108.08613</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given two strings S and P, the Episode Matching problem is to compute the length of the shortest substring of S that contains P as a subsequence. The best known upper bound for this problem is Õ(nm) by Das et al. (1997), where n,m are the lengths of S and P, respectively. Although the problem is well studied and has many applications in data mining, this bound has never been improved. In this paper we show why this is the case by proving that an O((nm)1−ϵ) algorithm (even for binary strings) would refute the popular Strong Exponential Time Hypothesis (SETH). The proof is based on a simple reduction from Orthogonal Vectors.
]]></description>
<dc:subject>edit-distance computational-complexity algorithms strings rather-interesting to-write-about consider:genetic-programming consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0462c88f827d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1804.10186">
    <title>[1804.10186] Edit Distance between Unrooted Trees in Cubic Time</title>
    <dc:date>2022-01-29T13:53:55+00:00</dc:date>
    <link>https://arxiv.org/abs/1804.10186</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on Algorithms, 6(1), 2009] showed how to compute the edit distance between rooted trees on n nodes in (n3) time. However, generalizing their method to unrooted trees seems quite problematic, and the most efficient known solution remains to be the previous (n3logn) time algorithm by Klein [ESA 1998]. Given the lack of progress on improving this complexity, it might appear that unrooted trees are simply more difficult than rooted trees. We show that this is, in fact, not the case, and edit distance between unrooted trees on n nodes can be computed in (n3) time. A significantly faster solution is unlikely to exist, as Bringmann et al. [SODA 2018] proved that the complexity of computing the edit distance between rooted trees cannot be decreased to (n3−ϵ) unless some popular conjecture fails, and the lower bound easily extends to unrooted trees. We also show that for two unrooted trees of size m and n, where m≤n, our algorithm can be modified to run in (nm2(1+lognm)). This, again, matches the complexity achieved by Demaine et al. for rooted trees, who also showed that this is optimal if we restrict ourselves to the so-called decomposition algorithms.
]]></description>
<dc:subject>edit-distance trees computational-complexity algorithms rather-interesting might-be-useful</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:37917acf2248/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:might-be-useful"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2111.05386">
    <title>[2111.05386] Computing Area-Optimal Simple Polygonizations</title>
    <dc:date>2022-01-28T12:07:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.05386</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical methods have received considerable attention. However, previous methods focused on heuristic methods, with no proof of optimality. We develop exact methods, based on a combination of geometry and integer programming. As a result, we are able to solve instances of up to n=25 points to provable optimality. While this extends the range of solvable instances by a considerable amount, it also illustrates the practical difficulty of both problem variants.
]]></description>
<dc:subject>computational-geometry computational-complexity out-of-the-box TSP variant-problems algorithms optimization to-write-about to-visualize consider:multiobjective</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:02d90f2612d1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:out-of-the-box"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:TSP"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:variant-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:multiobjective"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2111.02544">
    <title>[2111.02544] Polygon Placement Revisited: (Degree of Freedom + 1)-SUM Hardness and an Improvement via Offline Dynamic Rectangle Union</title>
    <dc:date>2022-01-27T17:39:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.02544</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We revisit the classical problem of determining the largest copy of a simple polygon P that can be placed into a simple polygon Q. Despite significant effort, known algorithms require high polynomial running times. (Barequet and Har-Peled, 2001) give a lower bound of n2−o(1) under the 3SUM conjecture when P and Q are (convex) polygons with Θ(n) vertices each. This leaves open whether we can establish (1) hardness beyond quadratic time and (2) any superlinear bound for constant-sized P or Q. 
In this paper, we affirmatively answer these questions under the kSUM conjecture, proving natural hardness results that increase with each degree of freedom (scaling, x-translation, y-translation, rotation): (1) Finding the largest copy of P that can be x-translated into Q requires time n2−o(1) under the 3SUM conjecture. (2) Finding the largest copy of P that can be arbitrarily translated into Q requires time n2−o(1) under the 4SUM conjecture. (3) The above lower bounds are almost tight when one of the polygons is of constant size: we obtain an Õ((pq)2.5)-time algorithm for orthogonal polygons P,Q with p and q vertices, respectively. (4) Finding the largest copy of P that can be arbitrarily rotated and translated into Q requires time n3−o(1) under the 5SUM conjecture. 
We are not aware of any other such natural (degree of freedom +1)-SUM hardness for a geometric optimization problem.
]]></description>
<dc:subject>computational-complexity computational-geometry algorithms rather-interesting optimization to-write-about to-visualize consider:genetic-programming consider:representation consider:hillclimbing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3dfb3cfccec1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:hillclimbing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2106.14020">
    <title>[2106.14020] An Improved Physical ZKP for Nonogram</title>
    <dc:date>2022-01-27T11:50:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2106.14020</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Nonogram is a logic puzzle consisting of a rectangular grid with an objective to color every cell black or white such that the lengths of blocks of consecutive black cells in each row and column are equal to the given numbers. In 2010, Chien and Hon developed the first physical zero-knowledge proof for Nonogram, which allows a prover to physically show that he/she knows a solution of the puzzle without revealing it. However, their protocol requires special tools such as scratch-off cards and a machine to seal the cards, which are difficult to find in everyday life. Their protocol also has a nonzero soundness error. In this paper, we propose a more practical physical zero-knowledge proof for Nonogram that uses only a deck of regular paper cards and also has perfect soundness.
]]></description>
<dc:subject>mathematical-recreations computational-complexity constraint-satisfaction rather-interesting algorithms to-write-about to-visualize consider:looking-to-see consider:sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4c16865388a3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1810.02241">
    <title>[1810.02241] Recursion schemes, discrete differential equations and characterization of polynomial time computation</title>
    <dc:date>2022-01-26T13:44:39+00:00</dc:date>
    <link>https://arxiv.org/abs/1810.02241</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations of complexity and computability classes. 
The proposed framework presents an original point of view on complexity and computability classes. It also unifies in an elegant settings various constructions that have been proposed for characterizing these classes. This includes Cobham's and, Bellantoni and Cook's definition of polynomial time and later extensions on the approach, as well as recent characterizations of computability and complexity by classes of ordinary differential equations. It also helps understanding the relationships between analog computations and classical discrete models of computation theory. 
At a more technical point of view, this paper points out the fundamental role of linear (discrete) ordinary differential equations and classical ODE tools such as changes of variables to capture computability and complexity measures, or as a tool for programming various algorithms.
]]></description>
<dc:subject>diffy-Qs discrete-mathematics nonlinear-dynamics representation rather-interesting computational-complexity models-and-modes to-understand to-write-about consider:genetic-programming consider:approximation ReQ</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b5692977ee6e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:diffy-Qs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrete-mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models-and-modes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ReQ"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2111.02992">
    <title>[2111.02992] The Shortest Even Cycle Problem is Tractable</title>
    <dc:date>2022-01-22T12:57:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2111.02992</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given a directed graph, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even cycle in a directed graph in polynomial time was open for more than two decades until Robertson, Seymour, and Thomas (Ann. of Math. (2) 1999) and, independently, McCuaig (Electron. J. Combin. 2004; announced jointly at STOC 1997) gave an efficiently testable structural characterisation of even-cycle-free directed graphs. 
Methodologically, our algorithm relies on algebraic fingerprinting and randomized polynomial identity testing over a finite field, and uses a generating polynomial implicit in Vazirani and Yannakakis ( Discrete Appl. Math. 1989) that enumerates weighted cycle covers as a difference of a permanent and a determinant polynomial. The need to work with the permanent is where our main technical contribution occurs. We design a family of finite commutative rings of characteristic 4 that simultaneously (i) give a nondegenerate representation for the generating polynomial identity via the permanent and the determinant, (ii) support efficient permanent computations, and (iii) enable emulation of finite-field arithmetic in characteristic 2. Here our work is foreshadowed by that of Björklund and Husfeldt (SIAM J. Comput. 2019), who used a considerably less efficient ring design to obtain a polynomial-time algorithm for the shortest two disjoint paths problem. 
Building on work of Gilbert and Tarjan (Numer. Math. 1978) as well as Alon and Yuster (J. ACM 2013), we also show how ideas from the nested dissection technique for solving linear equation systems leads to faster algorithm designs when we have control on the separator structure of the input graph; for example, this happens when the input has bounded genus.
]]></description>
<dc:subject>computational-complexity algorithms graph-theory rather-interesting nudge-targets consider:representation consider:rediscovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c79ed6a6c051/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.11695">
    <title>[2011.11695] Proximu$: Efficiently Scaling DNN Inference in Multi-core CPUs through Near-Cache Compute</title>
    <dc:date>2021-11-28T15:52:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.11695</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Deep Neural Network (DNN) inference is emerging as the fundamental bedrock for a multitude of utilities and services. CPUs continue to scale up their raw compute capabilities for DNN inference along with mature high performance libraries to extract optimal performance. While general purpose CPUs offer unique attractive advantages for DNN inference at both datacenter and edge, they have primarily evolved to optimize single thread performance. For highly parallel, throughput-oriented DNN inference, this results in inefficiencies in both power and performance, impacting both raw performance scaling and overall performance/watt. 
We present Proximu$, where we systematically tackle the root inefficiencies in power and performance scaling for CPU DNN inference. Performance scales efficiently by distributing light-weight tensor compute near all caches in a multi-level cache hierarchy. This maximizes the cumulative utilization of the existing bandwidth resources in the system and minimizes movement of data. Power is drastically reduced through simple ISA extensions that encode the structured, loop-y workload behavior. This enables a bulk offload of pre-decoded work, with loop unrolling in the light-weight near-cache units, effectively bypassing the power-hungry stages of the wide Out-of-Order (OOO) CPU pipeline. 
Across a number of DNN models, Proximu$ achieves a 2.3x increase in convolution performance/watt with a 2x to 3.94x scaling in raw performance. Similarly, Proximu$ achieves a 1.8x increase in inner-product performance/watt with 2.8x scaling in performance. With no changes to the programming model, no increase in cache capacity or bandwidth and minimal additional hardware, Proximu$ enables unprecedented CPU efficiency gains while achieving similar performance to state-of-the-art Domain Specific Accelerators (DSA) for DNN inference in this AI era.
]]></description>
<dc:subject>machine-learning distributed-processing rather-interesting algorithms computational-complexity sustainability optimization to-understand software-development-is-not-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8ed145e5333b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sustainability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development-is-not-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.03645#">
    <title>[1905.03645] Finding Optimal Longest Paths by Dynamic Programming in Parallel</title>
    <dc:date>2021-11-04T11:09:48+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.03645#</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art methods. This enables us to solve instances that were previously unsolved and solve hard instances significantly faster. Lastly, we present a scalable parallelization which yields the first efficient parallel algorithm for the problem.
]]></description>
<dc:subject>operations-research computational-complexity algorithms rather-interesting to-simulate to-visualize</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2411c7466dea/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2003.02605">
    <title>[2003.02605] Dynamic Approximate Maximum Independent Set of Intervals, Hypercubes and Hyperrectangles</title>
    <dc:date>2021-10-23T06:47:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2003.02605</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting. These graph classes include interval graphs and geometric intersection graphs, where vertices correspond to intervals/geometric objects and an edge indicates that the two corresponding objects intersect. 
We present dynamic approximation algorithms for independent set of intervals, hypercubes and hyperrectangles in d dimensions. They work in the fully dynamic model where each update inserts or deletes a geometric object. All our algorithms are deterministic and have worst-case update times that are polylogarithmic for constant d and ϵ>0, assuming that the coordinates of all input objects are in [0,N]d and each of their edges has length at least 1. We obtain the following results: 
∙ For weighted intervals, we maintain a (1+ϵ)-approximate solution. 
∙ For d-dimensional hypercubes we maintain a (1+ϵ)2d-approximate solution in the unweighted case and a O(2d)-approximate solution in the weighted case. Also, we show that for maintaining an unweighted (1+ϵ)-approximate solution one needs polynomial update time for d≥2 if the ETH holds. 
∙ For weighted d-dimensional hyperrectangles we present a dynamic algorithm with approximation ratio (1+ϵ)logd−1N.
]]></description>
<dc:subject>computational-complexity computational-geometry multiobjective-optimization rather-interesting to-write-about to-simulate consider:genetic-programming approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4cb39f59b01a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:multiobjective-optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.02735">
    <title>[2011.02735] Monadic second-order logic and the domino problem on self-similar graphs</title>
    <dc:date>2021-10-22T10:35:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.02735</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider the domino problem on Schreier graphs of self-similar groups, and more generally their monadic second-order logic. On the one hand, we prove that if the group is bounded then the graph's monadic second-order logic is decidable. This covers, for example, the Sierpiński gasket graphs and the Schreier graphs of the Basilica group. On the other hand, we already prove undecidability of the domino problem for a class of self-similar groups, answering a question by Barbieri and Sablik, and some examples including one of linear growth.
]]></description>
<dc:subject>group-theory graph-theory rather-interesting information-theory algorithms to-understand computational-complexity unanswerable-questions formal-languages</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:589ef3cd7bc6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:unanswerable-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1710.03702">
    <title>[1710.03702] Representations and evaluation strategies for feasibly approximable functions</title>
    <dc:date>2021-10-06T11:20:34+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.03702</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great speed in practice. We aim to resolve this apparent paradox by studying classes of functions which can be feasibly integrated and maximised, together with representations for these classes of functions which encode the information which is necessary to uniformly compute integral and maximum in polynomial time. The theoretical framework for this is the second-order complexity theory for operators in analysis which was introduced by Kawamura and Cook (2012). The representations we study are based on rigorous approximation by polynomials, piecewise polynomials, and rational functions. We compare these representations with respect to polytime reducibility as well as with respect to their ability to quickly evaluate symbolic expressions in a given language. We show that the representation based on rigorous approximation by piecewise polynomials is polytime equivalent to the representation based on rigorous approximation by rational functions. With this representation, all terms in a certain language, which is expressive enough to contain the maximum and integral of most functions of practical interest, can be evaluated in polynomial time. By contrast, both the representation based on polynomial approximation and the standard representation based on function evaluation, which implicitly underlies the Ko-Friedman result, require exponential time to evaluate certain terms in this language. We confirm our theoretical results by an implementation in Haskell, which provides some evidence that second-order polynomial time computability is similarly closely tied with practical feasibility as its first-order counterpart.
]]></description>
<dc:subject>computational-complexity rather-interesting looking-to-see optimization numeric-methods algorithms feature-extraction to-write-about consider:GP-for-extremization representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3128cd3a255e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numeric-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:GP-for-extremization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1702.05589">
    <title>[1702.05589] A Circuit-Based Approach to Efficient Enumeration</title>
    <dc:date>2021-10-06T11:08:05+00:00</dc:date>
    <link>https://arxiv.org/abs/1702.05589</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in knowledge compilation, a sub-area of artificial intelligence. We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the Hamming weight of each valuation. Moreover, valuations of constant Hamming weight can be enumerated with linear preprocessing and constant delay. 
Our results yield a framework for efficient enumeration that applies to all problems whose solutions can be compiled to structured d-DNNFs. In particular, we use it to recapture classical results in database theory, for factorized database representations and for MSO evaluation. This gives an independent proof of constant-delay enumeration for MSO formulae with first-order free variables on bounded-treewidth structures.
]]></description>
<dc:subject>enumeration optimization computational-complexity proxy-problems rather-interesting consider:GP-precompilation consider:vector-arithmetic</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6cd1255dd587/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proxy-problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:GP-precompilation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:vector-arithmetic"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.07842">
    <title>[1901.07842] The Firebreak Problem</title>
    <dc:date>2021-10-03T20:02:21+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.07842</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Suppose we have a network that is represented by a graph G. Potentially a fire (or other type of contagion) might erupt at some vertex of G. We are able to respond to this outbreak by establishing a firebreak at k other vertices of G, so that the fire cannot pass through these fortified vertices. The question that now arises is which k vertices will result in the greatest number of vertices being saved from the fire, assuming that the fire will spread to every vertex that is not fully behind the k vertices of the firebreak. This is the essence of the {\sc Firebreak} decision problem, which is the focus of this paper. We establish that the problem is intractable on the class of split graphs as well as on the class of bipartite graphs, but can be solved in linear time when restricted to graphs having constant-bounded treewidth, or in polynomial time when restricted to intersection graphs. We also consider some closely related problems.
]]></description>
<dc:subject>graph-theory feature-construction computational-complexity algorithms rather-interesting to-write-about to-visualize consider:random-sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:65803e19bf3a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-visualize"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:random-sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.10897">
    <title>[2107.10897] Griddings of permutations and hardness of pattern matching</title>
    <dc:date>2021-10-01T20:42:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.10897</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the complexity of the decision problem known as Permutation Pattern Matching, or PPM. The input of PPM consists of a pair of permutations τ (the `text') and π (the `pattern'), and the goal is to decide whether τ contains π as a subpermutation. On general inputs, PPM is known to be NP-complete by a result of Bose, Buss and Lubiw. In this paper, we focus on restricted instances of PPM where the text is assumed to avoid a fixed (small) pattern σ; this restriction is known as Av(σ)-PPM. It has been previously shown that Av(σ)-PPM is polynomial for any σ of size at most 3, while it is NP-hard for any σ containing a monotone subsequence of length four. 
In this paper, we present a new hardness reduction which allows us to show, in a uniform way, that Av(σ)-PPM is hard for every σ of size at least 6, for every σ of size 5 except the symmetry class of 41352, as well as for every σ symmetric to one of the three permutations 4321, 4312 and 4231. Moreover, assuming the exponential time hypothesis, none of these hard cases of Av(σ)-PPM can be solved in time 2o(n/logn). Previously, such conditional lower bound was not known even for the unconstrained PPM problem. 
On the tractability side, we combine the CSP approach of Guillemot and Marx with the structural results of Huczynska and Vatter to show that for any monotone-griddable permutation class C, PPM is polynomial when the text is restricted to a permutation from C.
]]></description>
<dc:subject>computational-complexity algorithms discrete-mathematics rather-interesting permutations to-understand to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2ea3990f786e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:discrete-mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:permutations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://publications.mfo.de/handle/mfo/1413">
    <title>Diophantine equations and why they are hard</title>
    <dc:date>2021-09-12T12:50:46+00:00</dc:date>
    <link>https://publications.mfo.de/handle/mfo/1413</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Diophantine equations are polynomial equations whose
 solutions are required to be integer numbers. They
 have captured the attention of mathematicians during
 millennia and are at the center of much of contemporary
 research. Some Diophantine equations are easy,
 while some others are truly difficult. After some time
 spent with these equations, it might seem that no
 matter what powerful methods we learn or develop,
 there will always be a Diophantine equation immune
 to them, which requires a new trick, a better idea, or
 a refined technique. In this snapshot we explain why.
]]></description>
<dc:subject>mathematics Diophantine-equations constraint-satisfaction explanation computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b0b1ee7fbd9b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Diophantine-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:explanation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1901.01930">
    <title>[1901.01930] Keeping CALM: When Distributed Consistency is Easy</title>
    <dc:date>2021-07-11T20:39:53+00:00</dc:date>
    <link>https://arxiv.org/abs/1901.01930</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A key concern in modern distributed systems is to avoid the cost of coordination while maintaining consistent semantics. Until recently, there was no answer to the question of when coordination is actually required. In this paper we present an informal introduction to the CALM Theorem, which answers this question precisely by moving up from traditional storage consistency to consider properties of programs. 
CALM is an acronym for "consistency as logical monotonicity". The CALM Theorem shows that the programs that have consistent, coordination-free distributed implementations are exactly the programs that can be expressed in monotonic logic. This theoretical result has practical implications for developers of distributed applications. We show how CALM provides a constructive application-level counterpart to conventional "systems" wisdom, such as the apparently negative results of the CAP Theorem. We also discuss ways that monotonic thinking can influence distributed systems design, and how new programming language designs and tools can help developers write consistent, coordination-free code.
]]></description>
<dc:subject>distributed-processing to-understand computer-science formalization programming-language computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f3379ddde585/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:distributed-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formalization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:programming-language"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.05548">
    <title>[2102.05548] Breaking the Quadratic Barrier for Matroid Intersection</title>
    <dc:date>2021-07-03T12:09:15+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.05548</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids 1=(V,1) and 2=(V,2) on a comment ground set V of n elements, and then we have to find the largest common independent set S∈1∩2 by making independence oracle queries of the form "Is S∈1?" or "Is S∈2?" for S⊆V. The goal is to minimize the number of queries. 
Beating the existing Õ(n2) bound, known as the quadratic barrier, is an open problem that captures the limits of techniques from two lines of work. The first one is the classic Cunningham's algorithm [SICOMP 1986], whose Õ(n2)-query implementations were shown by CLS+ [FOCS 2019] and Nguyen [2019]. The other one is the general cutting plane method of Lee, Sidford, and Wong [FOCS 2015]. The only progress towards breaking the quadratic barrier requires either approximation algorithms or a more powerful rank oracle query [CLS+ FOCS 2019]. No exact algorithm with o(n2) independence queries was known. 
In this work, we break the quadratic barrier with a randomized algorithm guaranteeing Õ(n9/5) independence queries with high probability, and a deterministic algorithm guaranteeing Õ(n11/6) independence queries. Our key insight is simple and fast algorithms to solve a graph reachability problem that arose in the standard augmenting path framework [Edmonds 1968]. Combining this with previous exact and approximation algorithms leads to our results.
]]></description>
<dc:subject>hypergraphs matroids computational-complexity algorithms constraint-satisfaction rather-interesting to-simulate to-write-about consider:extreme-cases</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a50861e75f13/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matroids"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:extreme-cases"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.09715">
    <title>[2012.09715] Approximating inverse cumulative distribution functions to produce approximate random variables</title>
    <dc:date>2021-06-27T10:12:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.09715</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are designed to be computationally inexpensive, and much cheaper than exact library functions, and thus highly suitable for use in Monte Carlo simulations. Two approximations are presented for the Gaussian distribution: a piecewise constant on equally spaced intervals, and a piecewise linear using geometrically decaying intervals. The error of the approximations are bounded and the convergence demonstrated, and the computational savings measured for C and C++ implementations. Implementations tailored for Intel and Arm hardwares are inspected, alongside hardware agnostic implementations built using OpenMP. The savings are incorporated into a nested multilevel Monte Carlo framework with the Euler-Maruyama scheme to exploit the speed ups without losing accuracy, offering speed ups by a factor of 5--7. These ideas are empirically extended to the Milstein scheme, and the Cox-Ingersoll-Ross process' non central chi-squared distribution, which offer speed ups by a factor of 250 or more.
]]></description>
<dc:subject>numerical-methods approximation rather-interesting simulation sampling performance-measure computational-complexity nudge-targets consider:representation consider:performance-measures consider:lexicase consider:extreme-values</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8ed61cde1044/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:lexicase"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:extreme-values"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.14035">
    <title>[2011.14035] cMinMax: A Fast Algorithm to Find the Corners of an N-dimensional Convex Polytope</title>
    <dc:date>2021-06-17T22:01:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.14035</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[During the last years, the emerging field of Augmented & Virtual Reality (AR-VR) has seen tremendousgrowth. At the same time there is a trend to develop low cost high-quality AR systems where computing poweris in demand. Feature points are extensively used in these real-time frame-rate and 3D applications, thereforeefficient high-speed feature detectors are necessary. Corners are such special features and often are used as thefirst step in the marker alignment in Augmented Reality (AR). Corners are also used in image registration andrecognition, tracking, SLAM, robot path finding and 2D or 3D object detection and retrieval. Therefore thereis a large number of corner detection algorithms but most of them are too computationally intensive for use inreal-time applications of any complexity. Many times the border of the image is a convex polygon. For thisspecial, but quite common case, we have developed a specific algorithm, cMinMax. The proposed algorithmis faster, approximately by a factor of 5 compared to the widely used Harris Corner Detection algorithm. Inaddition is highly parallelizable. The algorithm is suitable for the fast registration of markers in augmentedreality systems and in applications where a computationally efficient real time feature detector is necessary.The algorithm can also be extended to N-dimensional polyhedrons.
]]></description>
<dc:subject>computational-geometry 3d augmented-reality rather-interesting computational-complexity consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:182da50a9ab6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:3d"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:augmented-reality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1802.06478">
    <title>[1802.06478] An Efficient Local Search for the Minimum Independent Dominating Set Problem</title>
    <dc:date>2021-05-26T10:27:40+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.06478</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses k-swap as the neighborhood operation. Given a feasible solution S, it is the operation of obtaining another feasible solution by dropping exactly k vertices from S and then by adding any number of vertices to it. We show that, when k=2, (resp., k=3 and a given solution is minimal with respect to 2-swap), we can find an improved solution in the neighborhood or conclude that no such solution exists in O(nΔ) (resp., O(nΔ3)) time, where n denotes the number of vertices and Δ denotes the maximum degree. We develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively, where the plateau search examines solutions of the same size as the current solution that are obtainable by exchanging a solution vertex and a non-solution vertex. The algorithm is so effective that, among 80 DIMACS graphs, it updates the best-known solution size for five graphs and performs as well as existing methods for the remaining graphs.
]]></description>
<dc:subject>graph-theory algorithms computational-complexity to-write-about consider:visualization consider:genetic-programming</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:73463940e0aa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://proceedings.mlr.press/v48/lic16.html">
    <title>Fast k-Nearest Neighbour Search via Dynamic Continuous Indexing</title>
    <dc:date>2021-05-22T23:10:24+00:00</dc:date>
    <link>http://proceedings.mlr.press/v48/lic16.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We devise a new strategy that avoids partitioning the vector space and present a novel randomized algorithm that runs in time linear in dimensionality of the space and sub-linear in the intrinsic dimensionality and the size of the dataset and takes space constant in dimensionality of the space and linear in the size of the dataset. The proposed algorithm allows fine-grained control over accuracy and speed on a per-query basis, automatically adapts to variations in data density, supports dynamic updates to the dataset and is easy-to-implement. We show appealing theoretical properties and demonstrate empirically that the proposed algorithm outperforms locality-sensitivity hashing (LSH) in terms of approximation quality, speed and space efficiency.
]]></description>
<dc:subject>algorithms computational-complexity to-understand machine-learning rather-interesting efficiency</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fb58e2900767/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:efficiency"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1703.00440">
    <title>[1703.00440] Fast k-Nearest Neighbour Search via Prioritized DCI</title>
    <dc:date>2021-05-22T22:47:01+00:00</dc:date>
    <link>https://arxiv.org/abs/1703.00440</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dependence of query time on intrinsic dimensionality from exponential to sublinear. In this paper, we propose a variant of DCI, which we call Prioritized DCI, and show a remarkable improvement in the dependence of query time on intrinsic dimensionality. In particular, a linear increase in intrinsic dimensionality, or equivalently, an exponential increase in the number of points near a query, can be mostly counteracted with just a linear increase in space. We also demonstrate empirically that Prioritized DCI significantly outperforms prior methods. In particular, relative to Locality-Sensitive Hashing (LSH), Prioritized DCI reduces the number of distance evaluations by a factor of 14 to 116 and the memory consumption by a factor of 21.
]]></description>
<dc:subject>algorithms computational-complexity rather-interesting impressive-even to-understand consider:generalizations consider:fitness-sorting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:aabd18e64a5d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:impressive-even"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:generalizations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:fitness-sorting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.02483">
    <title>[2105.02483] Covering Convex Polygons by Two Congruent Disks</title>
    <dc:date>2021-05-19T11:01:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.02483</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an O(nlogn)-time algorithm for the two-center problem for a convex polygon, where n is the number of vertices of the polygon. This improves upon the previous best algorithm for the problem.
]]></description>
<dc:subject>plane-geometry optimization nudge-targets computational-geometry computational-complexity algorithms to-write-about to-simulate consider:landscape-duagrams</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fbc26f50a173/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:landscape-duagrams"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.01450">
    <title>[1906.01450] A Fast-Optimal Guaranteed Algorithm For Learning Sub-Interval Relationships in Time Series</title>
    <dc:date>2021-05-11T19:10:01+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.01450</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Traditional approaches focus on finding relationships between two entire time series, however, many interesting relationships exist in small sub-intervals of time and remain feeble during other sub-intervals. We define the notion of a sub-interval relationship (SIR) to capture such interactions that are prominent only in certain sub-intervals of time. To that end, we propose a fast-optimal guaranteed algorithm to find most interesting SIR relationship in a pair of time series. Lastly, we demonstrate the utility of our method in climate science domain based on a real-world dataset along with its scalability scope and obtain useful domain insights.
]]></description>
<dc:subject>machine-learning time-series representation algorithms computational-complexity to-understand consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:28aab9f52cb0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:time-series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://swift.org/blog/swift-collections/">
    <title>Swift.org - Introducing Swift Collections</title>
    <dc:date>2021-05-05T10:47:52+00:00</dc:date>
    <link>https://swift.org/blog/swift-collections/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I’m thrilled to announce Swift Collections, a new open-source package focused on extending the set of available Swift data structures. Like the Swift Algorithms and Swift Numerics packages before it, we’re releasing Swift Collections to help incubate new functionality for the Swift Standard Library.

The Swift Standard Library currently implements the three most essential general-purpose data structures: Array, Set and Dictionary. These are the right tool for a wide variety of use cases, and they are particularly well-suited for use as currency types. But sometimes, in order to efficiently solve a problem or to maintain an invariant, Swift programmers would benefit from a larger library of data structures.

We expect the Collections package to empower you to write faster and more reliable programs, with less effort.

]]></description>
<dc:subject>swift software-development library data-structures rather-interesting to-learn computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:cef2a999d61f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:swift"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:software-development"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-learn"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.05275">
    <title>[2012.05275] How many pop-stacks does it take to sort a permutation?</title>
    <dc:date>2021-03-17T20:21:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.05275</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Pop-stacks are variants of stacks that were introduced by Avis and Newborn in 1981. Coincidentally, a 1982 result of Unger implies that every permutation of length n can be sorted by n-1 passes through a deterministic pop-stack. We give a new proof of this result inspired by Knuth's zero-one principle.
]]></description>
<dc:subject>combinatorics algorithms computational-complexity rather-interesting to-write-about to-simulate consider:genetic-programming data-structures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1fdf091e1be9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:genetic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.05459">
    <title>[1904.05459] Constant factor approximations to edit distance on far input pairs in nearly linear time</title>
    <dc:date>2021-01-21T21:08:56+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.05459</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[For any T≥1, there are constants R=R(T)≥1 and ζ=ζ(T)>0 and a randomized algorithm that takes as input an integer n and two strings x,y of length at most n, and runs in time O(n1+1T) and outputs an upper bound U on the edit distance ED(x,y) that with high probability, satisfies U≤R(ED(x,y)+n1−ζ). In particular, on any input with ED(x,y)≥n1−ζ the algorithm outputs a constant factor approximation with high probability. 
A similar result has been proven independently by Brakensiek and Rubinstein (2019).
]]></description>
<dc:subject>strings edit-distance proof computational-complexity to-understand consider:looking-to-see consider:visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:ba05fdb80253/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:edit-distance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.quantamagazine.org/a-new-algorithm-for-graph-crossings-hiding-in-plain-sight-20200915/">
    <title>A New Algorithm for Graph Crossings, Hiding in Plain Sight | Quanta Magazine</title>
    <dc:date>2020-10-03T12:14:28+00:00</dc:date>
    <link>https://www.quantamagazine.org/a-new-algorithm-for-graph-crossings-hiding-in-plain-sight-20200915/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[What they belatedly recognized in October was that a flip that brings you closer to being able to add a new edge also brings the graph closer to resembling one of the good drawings they’d already identified. By showing that a series of flips inevitably moves a graph toward a favorable drawing, the new algorithm puts a backstop on the number of flips you could possibly need to perform before finding a way to insert an edge (provided the insertion is possible at all).

]]></description>
<dc:subject>see-prior-bookmark graph-theory computational-complexity graph-layout rather-interesting algorithms to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:38d10dff7d32/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:see-prior-bookmark"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-layout"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1911.03449">
    <title>[1911.03449] Fully-dynamic Planarity Testing in Polylogarithmic Time</title>
    <dc:date>2020-10-03T12:12:51+00:00</dc:date>
    <link>https://arxiv.org/abs/1911.03449</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given a dynamic graph subject to insertions and deletions of edges, a natural question is whether the graph presently admits a planar embedding. We give a deterministic fully-dynamic algorithm for general graphs, running in amortized O(log3n) time per edge insertion or deletion, that maintains a bit indicating whether or not the graph is presently planar. This is an exponential improvement over the previous best algorithm [Eppstein, Galil, Italiano, Spencer, 1996] which spends amortized O(n‾√) time per update.
]]></description>
<dc:subject>algorithms computational-complexity computational-geometry graph-theory rather-interesting to-understand to-write-about consider:rediscovery consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7a3792b8651e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1712.09617">
    <title>[1712.09617] On efficiently solvable cases of Quantum k-SAT</title>
    <dc:date>2020-09-27T11:59:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.09617</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been well-studied for special tractable cases, as well as from a parameterized complexity perspective, much less is known in similar settings for k-QSAT. Here, we study the open problem of computing satisfying assignments to k-QSAT instances which have a "matching" or "dimer covering"; this is an NP problem whose decision variant is trivial, but whose search complexity remains open. 
Our results fall into three directions, all of which relate to the "matching" setting: (1) We give a polynomial-time classical algorithm for k-QSAT when all qubits occur in at most two clauses. (2) We give a parameterized algorithm for k-QSAT instances from a certain non-trivial class, which allows us to obtain exponential speedups over brute force methods in some cases. This is achieved by reducing the problem to solving for a single root of a single univariate polynomial. (3) We conduct a structural graph theoretic study of 3-QSAT interaction graphs which have a "matching". We remark that the results of (2), in particular, introduce a number of new tools to the study of Quantum SAT, including graph theoretic concepts such as transfer filtrations and blow-ups from algebraic geometry.
]]></description>
<dc:subject>constraint-satisfaction combinatorics computational-complexity to-understand purdy-pitchers hypergraphs visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:228fc42310cc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:purdy-pitchers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1703.10293">
    <title>[1703.10293] Preserving Distances in Very Faulty Graphs</title>
    <dc:date>2020-07-15T13:46:05+00:00</dc:date>
    <link>https://arxiv.org/abs/1703.10293</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures, it makes sense to study fault-tolerant versions of the above structures. This turns out to be a surprisingly difficult task. For every small but arbitrary set of edge or vertex failures, the preservers and spanners need to contain {\em replacement paths} around the faulted set. In this paper we make substantial progress on fault tolerant preservers and additive spanners: 
(1) We present the first truly sub-quadratic size single-pair preservers in unweighted (possibly directed) graphs for \emph{any} fixed number f of faults. Our result indeed generalizes to the single-source case, and can be used to build new fault-tolerant additive spanners (for all pairs). 
(2) The size of the above single-pair preservers is O(n2−g(f)) for some positive function g, and grows to O(n2) for increasing f. We show that this is necessary even in undirected unweighted graphs, and even if you allow for a small additive error: If you aim at size O(n2−ϵ) for ϵ>0, then the additive error has to be $\Omega(\eps f)$. This surprisingly matches known upper bounds in the literature. 
(3) For weighted graphs, we provide matching upper and lower bounds for the single pair case. Namely, the size of the preserver is Θ(n2) for f≥2 in both directed and undirected graphs, while for f=1 the size is Θ(n) in undirected graphs. For directed graphs, we have a superlinear upper bound and a matching lower bound. 
Most of our lower bounds extend to the distance oracle setting, where rather than a subgraph we ask for any compact data structure.
]]></description>
<dc:subject>network-theory robustness rather-interesting algorithms computational-complexity graph-theory to-write-about to-simulate consider:looking-to-see consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:2475359bbfb8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2001.09575">
    <title>[2001.09575] On the Length of Monotone Paths in Polyhedra</title>
    <dc:date>2020-07-10T11:27:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2001.09575</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Motivated by the problem of bounding the number of iterations of the Simplex algorithm we investigate the possible lengths of monotone paths followed by the Simplex method inside the oriented graphs of polyhedra (oriented by the objective function). We consider both the shortest and the longest monotone paths and estimate the monotone diameter and height of polyhedra. Our analysis applies to transportation polytopes, matroid polytopes, matching polytopes, shortest-path polytopes, and the TSP, among others. We begin by showing that combinatorial cubes have monotone and Bland pivot height bounded by their dimension and that in fact all monotone paths of zonotopes are no larger than the number of edge directions of the zonotope. We later use this to show that several polytopes have polynomial-size pivot height, for all pivot rules. In contrast, we show that many well-known combinatorial polytopes have exponentially-long monotone paths. Surprisingly, for some famous pivot rules, e.g., greatest improvement and steepest edge, these same polytopes have polynomial-size simplex paths.
]]></description>
<dc:subject>computational-geometry extreme-values rather-interesting looking-to-see computational-complexity operations-research consider:looking-to-see to-simulate consider:oriented-gradients</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f739ddbc1403/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:extreme-values"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:operations-research"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:oriented-gradients"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2006.03045">
    <title>[2006.03045] Online Versus Offline Rate in Streaming Codes for Variable-Size Messages</title>
    <dc:date>2020-07-09T23:29:24+00:00</dc:date>
    <link>https://arxiv.org/abs/2006.03045</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Providing high quality-of-service for live communication is a pervasive challenge which is plagued by packet losses during transmission. Streaming codes are a class of erasure codes specifically designed for such low-latency streaming communication settings. We consider the recently proposed setting of streaming codes under variable-size messages which reflects the requirements of applications such as live video streaming. In practice, streaming codes often need to operate in an "online" setting where the sizes of the future messages are unknown. Yet, previously studied upper bounds on the rate apply to "offline" coding schemes with access to all (including future) message sizes. 
In this paper, we evaluate whether the optimal offline rate is a feasible goal for online streaming codes when communicating over a burst-only packet loss channel. We identify two broad parameter regimes where, perhaps surprisingly, online streaming codes can, in fact, match the optimal offline rate. For both of these settings, we present rate-optimal online code constructions. For all remaining parameter settings, we establish that it is impossible for online coding schemes to attain the optimal offline rate.
]]></description>
<dc:subject>information-theory online-learning optimization no-backsies algorithms rather-interesting computational-complexity to-simulate to-write-about consider:animation consider:working-up-to-it consider:performance-measures</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b5ac353a0001/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:online-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:no-backsies"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:animation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:working-up-to-it"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1803.08621">
    <title>[1803.08621] Parallel Range, Segment and Rectangle Queries with Augmented Maps</title>
    <dc:date>2020-05-30T14:07:26+00:00</dc:date>
    <link>https://arxiv.org/abs/1803.08621</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The range, segment and rectangle query problems are fundamental problems in computational geometry, and have extensive applications in many domains. Despite the significant theoretical work on these problems, efficient implementations can be complicated. We know of very few practical implementations of the algorithms in parallel, and most implementations do not have tight theoretical bounds. We focus on simple and efficient parallel algorithms and implementations for these queries, which have tight worst-case bound in theory and good parallel performance in practice. We propose to use a simple framework (the augmented map) to model the problem. Based on the augmented map interface, we develop both multi-level tree structures and sweepline algorithms supporting range, segment and rectangle queries in two dimensions. For the sweepline algorithms, we propose a parallel paradigm and show corresponding cost bounds. All of our data structures are work-efficient to build in theory and achieve a low parallel depth. The query time is almost linear to the output size. 
We have implemented all the data structures described in the paper using a parallel augmented map library. Based on the library each data structure only requires about 100 lines of C++ code. We test their performance on large data sets (up to 108 elements) and a machine with 72-cores (144 hyperthreads). The parallel construction achieves 32-68x speedup. Speedup numbers on queries are up to 126-fold. Our sequential implementation outperforms the CGAL library by at least 2x in both construction and queries. Our sequential implementation can be slightly slower than the R-tree in the Boost library in some cases (0.6-2.5x), but has significantly better query performance (1.6-1400x) than Boost.
]]></description>
<dc:subject>data-structures database computational-complexity computational-geometry rather-interesting algorithms to-understand to-write-about to-simulate consider:off-axis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:843cb9a19680/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:data-structures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:database"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:off-axis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.05720">
    <title>[1902.05720] Descriptive complexity for minimal time of cellular automata</title>
    <dc:date>2020-05-23T11:31:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.05720</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Descriptive complexity may be useful to design programs in a natural declarative way. This is important for parallel computation models such as cellular automata, because designing parallel programs is considered difficult. Our paper establishes logical characterizations of the three classical complexity classes that model minimal time, called real-time, of one-dimensional cellular automata according to their canonical variants. Our logics are natural restrictions of the existential second-order Horn logic. They correspond to the three ways of deciding a language on a square grid circuit of side n according to the three canonical placements of an input word of length n on the grid. Our key tool is a normalization method that transforms a formula into an equivalent formula that literally mimics a grid circuit.
]]></description>
<dc:subject>cellular-automata computational-complexity to-understand formal-languages representation algorithms classification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f6d3accd85a0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:cellular-automata"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:formal-languages"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1702.06976">
    <title>[1702.06976] Heavy-Tailed Analogues of the Covariance Matrix for ICA</title>
    <dc:date>2020-05-22T21:33:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1702.06976</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Independent Component Analysis (ICA) is the problem of learning a square matrix A, given samples of X=AS, where S is a random vector with independent coordinates. Most existing algorithms are provably efficient only when each Si has finite and moderately valued fourth moment. However, there are practical applications where this assumption need not be true, such as speech and finance. Algorithms have been proposed for heavy-tailed ICA, but they are not practical, using random walks and the full power of the ellipsoid algorithm multiple times. The main contributions of this paper are: 
(1) A practical algorithm for heavy-tailed ICA that we call HTICA. We provide theoretical guarantees and show that it outperforms other algorithms in some heavy-tailed regimes, both on real and synthetic data. Like the current state-of-the-art, the new algorithm is based on the centroid body (a first moment analogue of the covariance matrix). Unlike the state-of-the-art, our algorithm is practically efficient. To achieve this, we use explicit analytic representations of the centroid body, which bypasses the use of the ellipsoid method and random walks. 
(2) We study how heavy tails affect different ICA algorithms, including HTICA. Somewhat surprisingly, we show that some algorithms that use the covariance matrix or higher moments can successfully solve a range of ICA instances with infinite second moment. We study this theoretically and experimentally, with both synthetic and real-world heavy-tailed data.
]]></description>
<dc:subject>machine-learning benchmarking matrices rather-interesting to-write-about nudge-targets consider:representation consider:ReQ algorithms computational-complexity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d40bd17995ea/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:benchmarking"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:matrices"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:ReQ"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1705.01595">
    <title>[1705.01595] Homomorphisms Are a Good Basis for Counting Small Subgraphs</title>
    <dc:date>2020-05-22T21:22:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1705.01595</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lovász show that many interesting quantities have this form, including, for fixed graphs H, the number of H-copies (induced or not) in an input graph G, and the number of homomorphisms from H to G. 
Using the framework of graph motif parameters, we obtain faster algorithms for counting subgraph copies of fixed graphs H in host graphs G: For graphs H on k edges, we show how to count subgraph copies of H in time kO(k)⋅n0.174k+o(k) by a surprisingly simple algorithm. This improves upon previously known running times, such as O(n0.91k+c) time for k-edge matchings or O(n0.46k+c) time for k-cycles. 
Furthermore, we prove a general complexity dichotomy for evaluating graph motif parameters: Given a class  of such parameters, we consider the problem of evaluating f∈ on input graphs G, parameterized by the number of induced subgraphs that f depends upon. For every recursively enumerable class , we prove the above problem to be either FPT or #W[1]-hard, with an explicit dichotomy criterion. This allows us to recover known dichotomies for counting subgraphs, induced subgraphs, and homomorphisms in a uniform and simplified way, together with improved lower bounds. 
Finally, we extend graph motif parameters to colored subgraphs and prove a complexity trichotomy: For vertex-colored graphs H and G, where H is from a fixed class , we want to count color-preserving H-copies in G. We show that this problem is either polynomial-time solvable or FPT or #W[1]-hard, and that the FPT cases indeed need FPT time under reasonable assumptions.
]]></description>
<dc:subject>graph-theory feature-construction computational-complexity algorithms rather-interesting heuristics to-write-about to-simulate consider:representation consider:slow-algorithms-but-obvious</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:47778c23cce3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:heuristics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:slow-algorithms-but-obvious"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1804.02075">
    <title>[1804.02075] A Framework for Searching in Graphs in the Presence of Errors</title>
    <dc:date>2020-05-17T22:22:25+00:00</dc:date>
    <link>https://arxiv.org/abs/1804.02075</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We consider the problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each \emph{vertex-query} points to a vertex v and the response either admits v is the target or provides any neighbor s≠v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability p<1/2 and a correct one with probability 1−p). 
We study this problem in both adversarial errors and independent noise models. First, we show an algorithm that needs log2n1−H(r) queries against \emph{adversarial} errors, where adversary is bounded with its rate of errors by a known constant r<1/2. Our algorithm is in fact a simplification of previous work, and our refinement lies in invoking amortization argument. We then show that our algorithm coupled with Chernoff bound argument leads to an algorithm for independent noise that is simpler and with a query complexity that is both simpler and asymptotically better to one of Emamjomeh-Zadeh et al. [STOC 2016]. 
Our approach has a wide range of applications. First, it improves and simplifies Robust Interactive Learning framework proposed by Emamjomeh-Zadeh et al. [NIPS 2017]. Secondly, performing analogous analysis for \emph{edge-queries} (where query to edge e returns its endpoint that is closer to target) we actually recover (as a special case) noisy binary search algorithm that is asymptotically optimal, matching the complexity of Feige et al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon existing algorithm for searching of \emph{unbounded} domains due to Aslam and Dhagat [STOC 1991].
]]></description>
<dc:subject>graph-theory algorithms robustness error-correction rather-interesting to-write-about computational-complexity to-simulate consider:graph-structure</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b450a0214352/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:error-correction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:graph-structure"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>