Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing最新文献_第9页

Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs 马尔可夫链的近线性时间算法和有向图的新谱基元

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-11-02 DOI: 10.1145/3055399.3055463

Michael B. Cohen, Jonathan A. Kelner, John Peebles, Richard Peng, Anup B. Rao, Aaron Sidford, Adrian Vladu

{"title":"Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs","authors":"Michael B. Cohen, Jonathan A. Kelner, John Peebles, Richard Peng, Anup B. Rao, Aaron Sidford, Adrian Vladu","doi":"10.1145/3055399.3055463","DOIUrl":"https://doi.org/10.1145/3055399.3055463","url":null,"abstract":"In this paper, we begin to address the longstanding algorithmic gap between general and reversible Markov chains. We develop directed analogues of several spectral graph-theoretic tools that had previously been available only in the undirected setting, and for which it was not clear that directed versions even existed. In particular, we provide a notion of approximation for directed graphs, prove sparsifiers under this notion always exist, and show how to construct them in almost linear time. Using this notion of approximation, we design the first almost-linear-time directed Laplacian system solver, and, by leveraging the recent framework of [Cohen-Kelner-Peebles-Peng-Sidford-Vladu, FOCS '16], we also obtain almost-linear-time algorithms for computing the stationary distribution of a Markov chain, computing expected commute times in a directed graph, and more. For each problem, our algorithms improve the previous best running times of O((nm3/4 + n2/3 m) logO(1) (n κ ε-1)) to O((m + n2O(√lognloglogn)) logO(1) (n κε-1)) where n is the number of vertices in the graph, m is the number of edges, κ is a natural condition number associated with the problem, and ε is the desired accuracy. We hope these results open the door for further studies into directed spectral graph theory, and that they will serve as a stepping stone for designing a new generation of fast algorithms for directed graphs.","PeriodicalId":20615,"journal":{"name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89373473","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: 82

Information-theoretic thresholds from the cavity method 来自空腔方法的信息理论阈值

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-11-02 DOI: 10.1145/3055399.3055420

A. Coja-Oghlan, F. Krzakala, Will Perkins, L. Zdeborová

引用次数: 101

Efficient empirical revenue maximization in single-parameter auction environments 单参数拍卖环境下的有效经验收益最大化

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-31 DOI: 10.1145/3055399.3055427

Yannai A. Gonczarowski, N. Nisan

引用次数: 67

Subquadratic submodular function minimization 次二次次模函数最小化

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-31 DOI: 10.1145/3055399.3055419

Deeparnab Chakrabarty, Y. Lee, Aaron Sidford, Sam Chiu-wai Wong

{"title":"Subquadratic submodular function minimization","authors":"Deeparnab Chakrabarty, Y. Lee, Aaron Sidford, Sam Chiu-wai Wong","doi":"10.1145/3055399.3055419","DOIUrl":"https://doi.org/10.1145/3055399.3055419","url":null,"abstract":"Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer vision and machine learning, fast SFM algorithms are highly desirable. The current fastest algorithms [Lee, Sidford, Wong, 2015] run in O(n2lognM· EO + n3logO(1)nM) time and O(n3log2n· EO +n4logO(1)n)time respectively, where M is the largest absolute value of the function (assuming the range is integers) and is the time taken to evaluate the function on any set. Although the best known lower bound on the query complexity is only Ω(n) [Harvey, 2008], the current shortest non-deterministic proof [Cunningham, 1985] certifying the optimum value of a function requires Ω(n2) function evaluations. The main contribution of this paper are subquadratic SFM algorithms. For integer-valued submodular functions, we give an SFM algorithm which runs in O(nM3logn· EO) time giving the first nearly linear time algorithm in any known regime. For real-valued submodular functions with range in [-1,1], we give an algorithm which in Õ(n5/3· EO/ε2) time returns an ε-additive approximate solution. At the heart of it, our algorithms are projected stochastic subgradient descent methods on the Lovasz extension of submodular functions where we crucially exploit submodularity and data structures to obtain fast, i.e. sublinear time, subgradient updates. The latter is crucial for beating the n2 bound - we show that algorithms which access only subgradients of the Lovasz extension, and these include the empirically fast Fujishige-Wolfe heuristic [Fujishige, 1980; Wolfe, 1976]","PeriodicalId":20615,"journal":{"name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83215285","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: 39

The computational complexity of ball permutations 球排列的计算复杂性

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-21 DOI: 10.1145/3055399.3055453

S. Aaronson, Adam Bouland, G. Kuperberg, S. Mehraban

引用次数: 12

How well do local algorithms solve semidefinite programs? 局部算法解决半定程序的效果如何?

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-17 DOI: 10.1145/3055399.3055451

Z. Fan, A. Montanari

{"title":"How well do local algorithms solve semidefinite programs?","authors":"Z. Fan, A. Montanari","doi":"10.1145/3055399.3055451","DOIUrl":"https://doi.org/10.1145/3055399.3055451","url":null,"abstract":"Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing and yet poorly understood dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even sophisticated semi-definite programming (SDP) relaxations fail. In order to explore this phenomenon, we study a classical SDP relaxation of the minimum graph bisection problem, when applied to Erdos-Renyi random graphs with bounded average degree d > 1, and obtain several types of results. First, we use a dual witness construction (using the so-called non-backtracking matrix of the graph) to upper bound the SDP value. Second, we prove that a simple local algorithm approximately solves the SDP to within a factor 2d^2/(2d^2 + d - 1) of the upper bound. In particular, the local algorithm is at most 8/9 suboptimal, and 1 + O(d^-1) suboptimal for large degree. We then analyze a more sophisticated local algorithm, which aggregates information according to the harmonic measure on the limiting Galton-Watson (GW) tree. The resulting lower bound is expressed in terms of the conductance of the GW tree and matches surprisingly well the empirically determined SDP values on large-scale Erdos-Renyi graphs. We finally consider the planted partition model. In this case, purely local algorithms are known to fail, but they do succeed if a small amount of side information is available. Our results imply quantitative bounds on the threshold for partial recovery using SDP in this model.","PeriodicalId":20615,"journal":{"name":"Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79318744","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

Local max-cut in smoothed polynomial time 在光滑多项式时间内的局部极大割

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-16 DOI: 10.1145/3055399.3055402

Omer Angel, Sébastien Bubeck, Y. Peres, F. Wei

引用次数: 45

Approximate counting, the Lovasz local lemma, and inference in graphical models 图模型中的近似计数，Lovasz局部引理和推理

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-14 DOI: 10.1145/3055399.3055428

Ankur Moitra

引用次数: 45

Compression of quantum multi-prover interactive proofs 量子多证明者交互证明的压缩

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-10 DOI: 10.1145/3055399.3055441

Zhengfeng Ji

引用次数: 35

Approximating rectangles by juntas and weakly-exponential lower bounds for LP relaxations of CSPs 用集合逼近矩形和csp的LP松弛的弱指数下界

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing Pub Date : 2016-10-09 DOI: 10.1145/3055399.3055438

Pravesh Kothari, R. Meka, P. Raghavendra

引用次数: 73