ACM Transactions on Algorithms最新文献_第8页

Polynomial Kernel for Interval Vertex Deletion 区间顶点删除的多项式核

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2023-01-19 DOI: 10.1145/3571075

A. Agrawal, D. Lokshtanov, P. Misra, Saket Saurabh, M. Zehavi

引用次数: 0

On coalescence time in graphs–When is coalescing as fast as meeting? 论图的聚并时间——什么时候聚并和会合一样快?

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2023-01-17 DOI: https://dl.acm.org/doi/10.1145/3576900

Varun Kanade, Frederik Mallmann-Trenn, Thomas Sauerwald

{"title":"On coalescence time in graphs–When is coalescing as fast as meeting?","authors":"Varun Kanade, Frederik Mallmann-Trenn, Thomas Sauerwald","doi":"https://dl.acm.org/doi/10.1145/3576900","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3576900","url":null,"abstract":"Coalescing random walks is a fundamental distributed process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a single random walk. The coalescence time is defined as the expected time until only one particle remains, starting from one particle at every node. Despite recent progress such as by Cooper et al. [14] and Cooper et al. [19], the coalescence time for graphs such as binary trees, d-dimensional tori, hypercubes and more generally, vertex-transitive graphs, remains unresolved. We provide a powerful toolkit that results in tight bounds for various topologies including the aforementioned ones. The meeting time is defined as the worst-case expected time required for two random walks to arrive at the same node at the same time. As a general result, we establish that for graphs whose meeting time is only marginally larger than the mixing time (a factor of log 2n), the coalescence time of n random walks equals the meeting time up to constant factors. This upper bound is complemented by the construction of a graph family demonstrating that this result is the best possible up to constant factors. Finally, we prove a tight worst case bound for the coalescence time of O(n3). By duality, our results yield identical bounds on the voter model. Our techniques also yield a new bound on the hitting time and cover time of regular graphs, improving and tightening previous results by Broder and Karlin [12], as well as those by Aldous and Fill [2].","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"1 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

PTAS for Sparse General-valued CSPs 稀疏一般值csp的PTAS

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-12-13 DOI: 10.1145/3569956

Balázs F. Mezei, Marcin Wrochna, Stanislav Živný

{"title":"PTAS for Sparse General-valued CSPs","authors":"Balázs F. Mezei, Marcin Wrochna, Stanislav Živný","doi":"10.1145/3569956","DOIUrl":"https://doi.org/10.1145/3569956","url":null,"abstract":"We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker’s approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero, Wrochna, and Živný [SODA’21] showed that the Sherali-Adams LP relaxation gives a simple PTAS for all fractionally-treewidth-fragile classes, which is the most general “sparsity” condition for which a PTAS is known. We extend these results to general-valued CSPs, which include “crisp” (or “strict”) constraints that have to be satisfied by every feasible assignment. The only condition on the crisp constraints is that their domain contains an element that is at least as feasible as all the others (but possibly less valuable). For minimisation general-valued CSPs with crisp constraints, we present a PTAS for all Baker graph classes—a definition by Dvořák [SODA’20] that encompasses all classes where Baker’s technique is known to work, except for fractionally-treewidth-fragile classes. While this is standard for problems satisfying a certain monotonicity condition on crisp constraints, we show this can be relaxed to diagonalisability—a property of relational structures connected to logics, statistical physics, and random CSPs.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"19 1","pages":"1 - 31"},"PeriodicalIF":1.3,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48947945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Tightening Curves on Surfaces Monotonically with Applications 表面上单调的拧紧曲线与应用

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-11-11 DOI: https://dl.acm.org/doi/10.1145/3558097

Hsien-Chih Chang, Arnaud de Mesmay

{"title":"Tightening Curves on Surfaces Monotonically with Applications","authors":"Hsien-Chih Chang, Arnaud de Mesmay","doi":"https://dl.acm.org/doi/10.1145/3558097","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3558097","url":null,"abstract":"We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any time during the process. The best known upper bound before was exponential, which can be obtained by combining the algorithm of De Graaf and Schrijver [J. Comb. Theory Ser. B, 1997] together with an exponential upper bound on the number of possible surface maps. To obtain the new upper bound, we apply tools from hyperbolic geometry, as well as operations in graph drawing algorithms—the cluster and pipe expansions—to the study of curves on surfaces.As corollaries, we present two efficient algorithms for curves and graphs on surfaces. First, we provide a polynomial-time algorithm to convert any given multicurve on a surface into minimal position. Such an algorithm only existed for single closed curves, and it is known that previous techniques do not generalize to the multicurve case. Second, we provide a polynomial-time algorithm to reduce any k-terminal plane graph (and more generally, surface graph) using degree-1 reductions, series-parallel reductions, and Δ Y-transformations for arbitrary integer k. Previous algorithms only existed in the planar setting when k ≤ 4, and all of them rely on extensive case-by-case analysis based on different values of k. Our algorithm makes use of the connection between electrical transformations and homotopy moves and thus solves the problem in a unified fashion.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"1 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal Bound on the Combinatorial Complexity of Approximating Polytopes 逼近多面体组合复杂度的最优界

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-11-11 DOI: https://dl.acm.org/doi/10.1145/3559106

Rahul Arya, Sunil Arya, Guilherme D. da Fonseca, David Mount

{"title":"Optimal Bound on the Combinatorial Complexity of Approximating Polytopes","authors":"Rahul Arya, Sunil Arya, Guilherme D. da Fonseca, David Mount","doi":"https://dl.acm.org/doi/10.1145/3559106","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3559106","url":null,"abstract":"This article considers the question of how to succinctly approximate a multidimensional convex body by a polytope. Given a convex body K of unit diameter in Euclidean d-dimensional space (where d is a constant) and an error parameter ε > 0, the objective is to determine a convex polytope of low combinatorial complexity whose Hausdorff distance from K is at most ε. By combinatorial complexity, we mean the total number of faces of all dimensions. Classical constructions by Dudley and Bronshteyn/Ivanov show that O(1/ε(d-1)/2) facets or vertices are possible, respectively, but neither achieves both bounds simultaneously. In this article, we show that it is possible to construct a polytope with O(1/ε(d-1)/2) combinatorial complexity, which is optimal in the worst case.Our result is based on a new relationship between ε-width caps of a convex body and its polar body. Using this relationship, we are able to obtain a volume-sensitive bound on the number of approximating caps that are “essentially different.” We achieve our main result by combining this with a variant of the witness-collector method and a novel variable-thickness layered construction of the economical cap covering.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"1 8‐9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Introduction to the Special Issue on ACM-SIAM Symposium on Discrete Algorithms (SODA) 2020 ACM-SIAM离散算法研讨会(SODA) 2020特刊简介

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-11-11 DOI: https://dl.acm.org/doi/10.1145/3561912

Gautam Kamath, Sepehr Assadi, Anne Driemel, Janardhan Kulkarni

引用次数: 0

Introduction to the Special Issue on ACM-SIAM Symposium on Discrete Algorithms (SODA) 2020 ACM-SIAM离散算法研讨会（SODA）2020特刊简介

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-31 DOI: 10.1145/3561912

Gautam Kamath, Sepehr Assadi, A. Driemel, Janardhan Kulkarni

引用次数: 0

Minimum Cut and Minimum k-Cut in Hypergraphs via Branching Contractions 分支收缩超图中的最小割和最小k割

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-29 DOI: https://dl.acm.org/doi/10.1145/3570162

Kyle Fox, Debmalya Panigrahi, Fred Zhang

{"title":"Minimum Cut and Minimum k-Cut in Hypergraphs via Branching Contractions","authors":"Kyle Fox, Debmalya Panigrahi, Fred Zhang","doi":"https://dl.acm.org/doi/10.1145/3570162","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3570162","url":null,"abstract":"On hypergraphs with m hyperedges and n vertices, where p denotes the total size of the hyperedges, we provide the following results: <table border=\"0\" list-type=\"bullet\" width=\"95%\"><tr><td valign=\"top\">•</td><td colspan=\"5\" valign=\"top\">We give an algorithm that runs in (widetilde{O}left(mn^{2k-2}right) ) time for finding a minimum k-cut in hypergraphs of arbitrary rank. This algorithm betters the previous best running time for the minimum k-cut problem, for k > 2.</td></tr><tr><td valign=\"top\">•</td><td colspan=\"5\" valign=\"top\">We give an algorithm that runs in (widetilde{O}left(n^{max lbrace r,2k-2rbrace }right) ) time for finding a minimum k-cut in hypergraphs of constant rank r. This algorithm betters the previous best running times for both the minimum cut and minimum k-cut problems for dense hypergraphs.</td></tr></table>\u0000Both of our algorithms are Monte Carlo, i.e., they return a minimum k-cut (or minimum cut) with high probability. These algorithms are obtained as instantiations of a generic branching randomized contraction technique on hypergraphs, which extends the celebrated work of Karger and Stein on recursive contractions in graphs. Our techniques and results also extend to the problems of minimum hedge-cut and minimum hedge-k-cut on hedgegraphs, which generalize hypergraphs.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"2 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Lower Bound on Cycle-Finding in Sparse Digraphs 稀疏有向图中循环查找的下界

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3417979

Xi Chen, Tim Randolph, Rocco A. Servedio, Timothy Sun

引用次数: 0

Detecting Feedback Vertex Sets of Size k in O⋆ (2.7k) Time 在O -美女(2.7k)中检测大小为k的反馈顶点集

IF 1.3 3区计算机科学

ACM Transactions on Algorithms Pub Date : 2022-10-10 DOI: https://dl.acm.org/doi/10.1145/3504027

Jason Li, Jesper Nederlof

{"title":"Detecting Feedback Vertex Sets of Size k in O⋆ (2.7k) Time","authors":"Jason Li, Jesper Nederlof","doi":"https://dl.acm.org/doi/10.1145/3504027","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3504027","url":null,"abstract":"In the Feedback Vertex Set (FVS) problem, one is given an undirected graph G and an integer k, and one needs to determine whether there exists a set of k vertices that intersects all cycles of G (a so-called feedback vertex set). Feedback Vertex Set is one of the most central problems in parameterized complexity: It served as an excellent testbed for many important algorithmic techniques in the field such as Iterative Compression [Guo et al. (JCSS’06)], Randomized Branching [Becker et al. (J. Artif. Intell. Res’00)] and Cut&Count [Cygan et al. (FOCS’11)]. In particular, there has been a long race for the smallest dependence f(k) in run times of the type O⋆ (f(k)), where the O⋆ notation omits factors polynomial in n. This race seemed to have reached a conclusion in 2011, when a randomized O⋆ (3k) time algorithm based on Cut&Count was introduced.In this work, we show the contrary and give a O⋆ (2.7k) time randomized algorithm. Our algorithm combines all mentioned techniques with substantial new ideas: First, we show that, given a feedback vertex set of size k of bounded average degree, a tree decomposition of width (1-Ω (1))k can be found in polynomial time. Second, we give a randomized branching strategy inspired by the one from [Becker et al. (J. Artif. Intell. Res’00)] to reduce to the aforementioned bounded average degree setting. Third, we obtain significant run time improvements by employing fast matrix multiplication.","PeriodicalId":50922,"journal":{"name":"ACM Transactions on Algorithms","volume":"1 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0