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Proceedings of the forty-seventh annual ACM symposium on Theory of Computing最新文献

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Boolean Function Monotonicity Testing Requires (Almost) n 1/2 Non-adaptive Queries 布尔函数单调性测试需要(几乎)n 1/2非自适应查询
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-12-17 DOI: 10.1145/2746539.2746570
Xi Chen, Anindya De, R. Servedio, Li-Yang Tan
{"title":"Boolean Function Monotonicity Testing Requires (Almost) n 1/2 Non-adaptive Queries","authors":"Xi Chen, Anindya De, R. Servedio, Li-Yang Tan","doi":"10.1145/2746539.2746570","DOIUrl":"https://doi.org/10.1145/2746539.2746570","url":null,"abstract":"We prove a lower bound of Ω(n1/2-c), for all c> 0, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an n-variable Boolean function is monotone versus constant-far from monotone. This improves a ~Ω(n1/5) lower bound for the same problem that was obtained in [6], and is very close to the recent upper bound of ~O(n1/2/ε2) by Khot et al. [13].","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75839940","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: 53
On the Complexity of Nash Equilibria in Anonymous Games 论匿名博弈中纳什均衡的复杂性
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-12-17 DOI: 10.1145/2746539.2746571
X. Chen, D. Durfee, Anthi Orfanou
{"title":"On the Complexity of Nash Equilibria in Anonymous Games","authors":"X. Chen, D. Durfee, Anthi Orfanou","doi":"10.1145/2746539.2746571","DOIUrl":"https://doi.org/10.1145/2746539.2746571","url":null,"abstract":"We show that the problem of finding an ε-approximate Nash equilibrium in an {anonymous} game with seven pure strategies is complete in PPAD, when the approximation parameter ε is exponentially small in the number of players.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81166115","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: 24
Beyond the Euler Characteristic: Approximating the Genus of General Graphs 超越欧拉特征:逼近一般图的格
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-12-04 DOI: 10.1145/2746539.2746583
K. Kawarabayashi, Anastasios Sidiropoulos
{"title":"Beyond the Euler Characteristic: Approximating the Genus of General Graphs","authors":"K. Kawarabayashi, Anastasios Sidiropoulos","doi":"10.1145/2746539.2746583","DOIUrl":"https://doi.org/10.1145/2746539.2746583","url":null,"abstract":"Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by Thomassen [27] and a linear-time fixed-parameter algorithm has been obtained by Mohar [20]. Despite extensive study, the approximability of the Euler genus remains wide open. While the existence of a constant factor approximation is not ruled out, the currently best-known upper bound is a trivial O(n/g)-approximation that follows from bounds on the Euler characteristic. In this paper, we give the first non-trivial approximation algorithm for this problem. Specifically, we present a polynomial-time algorithm which given a graph G of Euler genus g outputs an embedding of G into a surface of Euler genus gO(1). Combined with the above O(n/g)-approximation, our result also implies a O(n1-α)-approximation, for some universal constant α> 0. Our approximation algorithm also has implications for the design of algorithms on graphs of small genus. Several of these algorithms require that an embedding of the graph into a surface of small genus is given as part of the input. Our result implies that many of these algorithms can be implemented even when the embedding of the input graph is unknown.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85151606","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: 10
Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs 完备和完备k部图相关聚类的近最优LP舍入算法
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-12-01 DOI: 10.1145/2746539.2746604
Shuchi Chawla, K. Makarychev, T. Schramm, G. Yaroslavtsev
{"title":"Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs","authors":"Shuchi Chawla, K. Makarychev, T. Schramm, G. Yaroslavtsev","doi":"10.1145/2746539.2746604","DOIUrl":"https://doi.org/10.1145/2746539.2746604","url":null,"abstract":"We give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps: For complete graphs our approximation is 2.06 - ε, which almost matches the previously known integrality gap of 2. For complete k-partite graphs our approximation is 3. We also show a matching integrality gap. For complete graphs with edge weights satisfying triangle inequalities and probability constraints, our approximation is 1.5, and we show an integrality gap of 1.2. Our results improve a long line of work on approximation algorithms for correlation clustering in complete graphs, previously culminating in a ratio of 2.5 for the complete case by Ailon, Charikar and Newman (JACM'08). In the weighted complete case satisfying triangle inequalities and probability constraints, the same authors give a 2-approximation; for the bipartite case, Ailon, Avigdor-Elgrabli, Liberty and van Zuylen give a 4-approximation (SICOMP'12).","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"2016 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86114248","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: 96
Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false) 编辑距离不能在强次二次时间内计算(除非SETH为假)
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-30 DOI: 10.1145/2746539.2746612
A. Backurs, P. Indyk
{"title":"Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)","authors":"A. Backurs, P. Indyk","doi":"10.1145/2746539.2746612","DOIUrl":"https://doi.org/10.1145/2746539.2746612","url":null,"abstract":"The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance between two strings is a classical computational task, with a well-known algorithm based on dynamic programming. Unfortunately, all known algorithms for this problem run in nearly quadratic time. In this paper we provide evidence that the near-quadratic running time bounds known for the problem of computing edit distance might be {tight}. Specifically, we show that, if the edit distance can be computed in time O(n2-δ) for some constant δ>0, then the satisfiability of conjunctive normal form formulas with N variables and M clauses can be solved in time MO(1) 2(1-ε)N for a constant ε>0. The latter result would violate the Strong Exponential Time Hypothesis, which postulates that such algorithms do not exist.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90585878","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: 379
FPTAS for #BIS with Degree Bounds on One Side 在一侧有度界的#BIS的FPTAS
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-28 DOI: 10.1145/2746539.2746598
Jingcheng Liu, P. Lu
{"title":"FPTAS for #BIS with Degree Bounds on One Side","authors":"Jingcheng Liu, P. Lu","doi":"10.1145/2746539.2746598","DOIUrl":"https://doi.org/10.1145/2746539.2746598","url":null,"abstract":"Counting the number of independent sets for a bipartite graph (#BIS) plays a crucial role in the study of approximate counting. It has been conjectured that there is no fully polynomial-time (randomized) approximation scheme (FPTAS/FPRAS) for #BIS, and it was proved that the problem for instances with a maximum degree of 6 is already as hard as the general problem. In this paper, we obtain a surprising tractability result for a family of #BIS instances. We design a very simple deterministic fully polynomial-time approximation scheme (FPTAS) for #BIS when the maximum degree for one side is no larger than 5. There is no restriction for the degrees on the other side, which do not even have to be bounded by a constant. Previously, FPTAS was only known for instances with a maximum degree of 5 for both sides.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"179 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80090318","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: 24
Randomized Rounding for the Largest Simplex Problem 最大单纯形问题的随机舍入
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-28 DOI: 10.1145/2746539.2746628
Aleksandar Nikolov
{"title":"Randomized Rounding for the Largest Simplex Problem","authors":"Aleksandar Nikolov","doi":"10.1145/2746539.2746628","DOIUrl":"https://doi.org/10.1145/2746539.2746628","url":null,"abstract":"The maximum volume j-simplex problem asks to compute the j-dimensional simplex of maximum volume inside the convex hull of a given set of n points in Qd. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of ej/2 + o(j). The problem is known to be NP-hard to approximate within a factor of cj for some constant c > 1. Our algorithm also gives a factor ej + o(j) approximation for the problem of finding the principal j x j submatrix of a rank d positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the D-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76488929","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: 59
Almost Optimal Pseudorandom Generators for Spherical Caps: Extended Abstract 球面帽的几乎最优伪随机发生器:扩展摘要
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-23 DOI: 10.1145/2746539.2746611
Pravesh Kothari, R. Meka
{"title":"Almost Optimal Pseudorandom Generators for Spherical Caps: Extended Abstract","authors":"Pravesh Kothari, R. Meka","doi":"10.1145/2746539.2746611","DOIUrl":"https://doi.org/10.1145/2746539.2746611","url":null,"abstract":"Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g., randomized rounding). We give an explicit PRG which fools spherical caps within error ε and has an almost optimal seed-length of O(log n + log(1/ε) ⋅ log log(1/ε)). For an inverse-polynomially growing error ε, our generator has a seed-length optimal up to a factor of O( log log (n)). The most efficient PRG previously known (due to Kane 2012) requires a seed-length of Ω(log3/2(n)) in this setting. We also obtain similar constructions to fool halfspaces with respect to the Gaussian distribution. Our construction and analysis are significantly different from previous works on PRGs for halfspaces and build on the iterative dimension reduction ideas of Kane et. al. 2011 and Celis et. al. 2013, the classical moment problem from probability theory and explicit constructions of approximate orthogonal designs based on the seminal work of Bourgain and Gamburd 2011 on expansion in Lie groups.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79333351","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: 17
Lower Bounds on the Size of Semidefinite Programming Relaxations 半定规划松弛大小的下界
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-23 DOI: 10.1145/2746539.2746599
James R. Lee, P. Raghavendra, David Steurer
{"title":"Lower Bounds on the Size of Semidefinite Programming Relaxations","authors":"James R. Lee, P. Raghavendra, David Steurer","doi":"10.1145/2746539.2746599","DOIUrl":"https://doi.org/10.1145/2746539.2746599","url":null,"abstract":"We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on n-vertex graphs are not the linear image of the feasible region of any SDP (i.e., any spectrahedron) of dimension less than 2nδ, for some constant δ > 0. This result yields the first super-polynomial lower bounds on the semidefinite extension complexity of any explicit family of polytopes. Our results follow from a general technique for proving lower bounds on the positive semidefinite rank of a matrix. To this end, we establish a close connection between arbitrary SDPs and those arising from the sum-of-squares SDP hierarchy. For approximating maximum constraint satisfaction problems, we prove that SDPs of polynomial-size are equivalent in power to those arising from degree-O(1) sum-of-squares relaxations. This result implies, for instance, that no family of polynomial-size SDP relaxations can achieve better than a 7/8-approximation for max-sat.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79872293","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: 181
Efficiently Learning Ising Models on Arbitrary Graphs 有效地学习任意图上的Ising模型
Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-11-22 DOI: 10.1145/2746539.2746631
Guy Bresler
{"title":"Efficiently Learning Ising Models on Arbitrary Graphs","authors":"Guy Bresler","doi":"10.1145/2746539.2746631","DOIUrl":"https://doi.org/10.1145/2746539.2746631","url":null,"abstract":"graph underlying an Ising model from i.i.d. samples. Over the last fifteen years this problem has been of significant interest in the statistics, machine learning, and statistical physics communities, and much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models. Nevertheless, for learning Ising models on general graphs with p nodes of degree at most d, it is not known whether or not it is possible to improve upon the pd computation needed to exhaustively search over all possible neighborhoods for each node. In this paper we show that a simple greedy procedure allows to learn the structure of an Ising model on an arbitrary bounded-degree graph in time on the order of p2. We make no assumptions on the parameters except what is necessary for identifiability of the model, and in particular the results hold at low-temperatures as well as for highly non-uniform models. The proof rests on a new structural property of Ising models: we show that for any node there exists at least one neighbor with which it has a high mutual information.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84567216","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: 178
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