Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing最新文献_第2页

Log-concave polynomials in theory and applications (tutorial) 对数凹多项式的理论与应用(教程)

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3465351

Nima Anari, C. Vinzant

引用次数: 0

Support of closed walks and second eigenvalue multiplicity of graphs 图的闭行走支持和第二特征值多重性

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451129

Theo McKenzie, P. M. R. Rasmussen, N. Srivastava

引用次数: 4

Dynamic planar point location in optimal time 在最佳时间内动态平面点定位

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451100

Yakov Nekrich

引用次数: 1

An improved derandomization of the switching lemma 一种改进的开关引理的非随机化

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451054

Zander Kelley

引用次数: 6

A framework for dynamic matching in weighted graphs 加权图的动态匹配框架

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451113

A. Bernstein, Aditi Dudeja, Zachary Langley

{"title":"A framework for dynamic matching in weighted graphs","authors":"A. Bernstein, Aditi Dudeja, Zachary Langley","doi":"10.1145/3406325.3451113","DOIUrl":"https://doi.org/10.1145/3406325.3451113","url":null,"abstract":"We introduce a new framework for computing approximate maximum weight matchings. Our primary focus is on the fully dynamic setting, where there is a large gap between the guarantees of the best known algorithms for computing weighted and unweighted matchings. Indeed, almost all current weighted matching algorithms that reduce to the unweighted problem lose a factor of two in the approximation ratio. In contrast, in other sublinear models such as the distributed and streaming models, recent work has largely closed this weighted/unweighted gap. For bipartite graphs, we almost completely settle the gap with a general reduction that converts any algorithm for α-approximate unweighted matching to an algorithm for (1−)α-approximate weighted matching, while only increasing the update time by an O(logn) factor for constant . We also show that our framework leads to significant improvements for non-bipartite graphs, though not in the form of a universal reduction. In particular, we give two algorithms for weighted non-bipartite matching: 1. A randomized (Las Vegas) fully dynamic algorithm that maintains a (1/2−)-approximate maximum weight matching in worst-case update time O(polylog n) with high probability against an adaptive adversary. Our bounds are essentially the same as those of the unweighted algorithm of Wajc [STOC 2020]. 2. A deterministic fully dynamic algorithm that maintains a (2/3−)-approximate maximum weight matching in amortized update time O(m1/4). Our bounds are essentially the same as those of the unweighted algorithm of Bernstein and Stein [SODA 2016]. A key feature of our framework is that it uses existing algorithms for unweighted matching as black-boxes. As a result, our framework is simple and versatile. Moreover, our framework easily translates to other models, and we use it to derive new results for the weighted matching problem in streaming and communication complexity models.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129675974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Approximate Gomory–Hu tree is faster than n – 1 max-flows 近似Gomory-Hu树比n - 1最大流更快

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451112

Jason Li, Debmalya Panigrahi

{"title":"Approximate Gomory–Hu tree is faster than n – 1 max-flows","authors":"Jason Li, Debmalya Panigrahi","doi":"10.1145/3406325.3451112","DOIUrl":"https://doi.org/10.1145/3406325.3451112","url":null,"abstract":"The Gomory-Hu tree or cut tree (Gomory and Hu, 1961) is a classic data structure for reporting s−t mincuts (and by duality, the values of s−t maxflows) for all pairs of vertices s and t in an undirected graph. Gomory and Hu showed that it can be computed using n−1 exact maxflow computations. Surprisingly, this remains the best algorithm for Gomory-Hu trees more than 50 years later, even for approximate mincuts. In this paper, we break this longstanding barrier and give an algorithm for computing a (1+є)-approximate Gomory-Hu tree using log(n) maxflow computations. Specifically, we obtain the runtime bounds we describe below. We obtain a randomized (Monte Carlo) algorithm for undirected, weighted graphs that runs in Õ(m + n3/2) time and returns a (1+є)-approximate Gomory-Hu tree algorithm whp. Previously, the best running time known was Õ(n5/2), which is obtained by running Gomory and Hu’s original algorithm on a cut sparsifier of the graph. Next, we obtain a randomized (Monte Carlo) algorithm for undirected, unweighted graphs that runs in m4/3+o(1) time and returns a (1+є)-approximate Gomory-Hu tree algorithm whp. This improves on our first result for sparse graphs, namely m = o(n9/8). Previously, the best running time known for unweighted graphs was Õ(mn) for an exact Gomory-Hu tree (Bhalgat et al., STOC 2007); no better result was known if approximations are allowed. As a consequence of our Gomory-Hu tree algorithms, we also solve the (1+є)-approximate all pairs mincut and single source mincut problems in the same time bounds. (These problems are simpler in that the goal is to only return the s−t mincut values, and not the mincuts.) This improves on the recent algorithm for these problems in Õ(n2) time due to Abboud et al. (FOCS 2020).","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125701674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

Near-linear time decoding of Ta-Shma’s codes via splittable regularity 利用可分正则性对Ta-Shma码进行近线性时间解码

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451126

F. G. Jeronimo, S. Srivastava, Madhur Tulsiani

{"title":"Near-linear time decoding of Ta-Shma’s codes via splittable regularity","authors":"F. G. Jeronimo, S. Srivastava, Madhur Tulsiani","doi":"10.1145/3406325.3451126","DOIUrl":"https://doi.org/10.1145/3406325.3451126","url":null,"abstract":"The Gilbert–Varshamov bound non-constructively establishes the existence of binary codes of distance 1/2−є/2 and rate Ω(є2). In a breakthrough result, Ta-Shma [STOC 2017] constructed the first explicit family of nearly optimal binary codes with distance 1/2−є/2 and rate Ω(є2+α), where α → 0 as є → 0. Moreover, the codes in Ta-Shma’s construction are є-balanced, where the distance between distinct codewords is not only bounded from below by 1/2−є/2, but also from above by 1/2+є/2. Polynomial time decoding algorithms for (a slight modification of) Ta-Shma’s codes appeared in [FOCS 2020], and were based on the Sum-of-Squares (SoS) semidefinite programming hierarchy. The running times for these algorithms were of the form NOα(1) for unique decoding, and NOє,α(1) for the setting of “gentle list decoding”, with large exponents of N even when α is a fixed constant. We derive new algorithms for both these tasks, running in time Õє(N). Our algorithms also apply to the general setting of decoding direct-sum codes. Our algorithms follow from new structural and algorithmic results for collections of k-tuples (ordered hypergraphs) possessing a “structured expansion” property, which we call splittability. This property was previously identified and used in the analysis of SoS-based decoding and constraint satisfaction algorithms, and is also known to be satisfied by Ta-Shma’s code construction. We obtain a new weak regularity decomposition for (possibly sparse) splittable collections W ⊆ [n]k, similar to the regularity decomposition for dense structures by Frieze and Kannan [FOCS 1996]. These decompositions are also computable in near-linear time Õ(|W |), and form a key component of our algorithmic results.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133713130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Learnability can be independent of set theory (invited paper) 可学习性可以独立于集合论(特邀论文)

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3465360

Shai Ben-David, P. Hrubes, S. Moran, Amir Shpilka, A. Yehudayoff

{"title":"Learnability can be independent of set theory (invited paper)","authors":"Shai Ben-David, P. Hrubes, S. Moran, Amir Shpilka, A. Yehudayoff","doi":"10.1145/3406325.3465360","DOIUrl":"https://doi.org/10.1145/3406325.3465360","url":null,"abstract":"A fundamental result in statistical learning theory is the equivalence of PAC learnability of a class with the finiteness of its Vapnik-Chervonenkis dimension. However, this clean result applies only to binary classification problems. In search for a similar combinatorial characterization of learnability in a more general setting, we discovered a surprising independence of set theory for some basic general notion of learnability. Consider the following statistical estimation problem: given a family F of real valued random variables over some domain X and an i.i.d. sample drawn from an unknown distribution P over X, find f in F such that its expectation w.r.t. P is close to the supremum expectation over all members of F. This Expectation Maximization (EMX) problem captures many well studied learning problems. Surprisingly, we show that the EMX learnability of some simple classes depends on the cardinality of the continuum and is therefore independent of the set theory ZFC axioms. Our results imply that that there exist no \"finitary\" combinatorial parameter that characterizes EMX learnability in a way similar to the VC-dimension characterization of binary classification learnability.","PeriodicalId":132752,"journal":{"name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133133959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strong co-nondeterministic lower bounds for NP cannot be proved feasibly NP的强共不确定性下界不能证明是可行的

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451117

J. Pich, R. Santhanam

引用次数: 7

Fiber bundle codes: breaking the n1/2 polylog(n) barrier for Quantum LDPC codes 光纤束码:突破量子LDPC码的n /2多对数(n)障碍

Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2021-06-15 DOI: 10.1145/3406325.3451005

M. Hastings, Jeongwan Haah, R. O'Donnell

引用次数: 80