2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)最新文献_第7页

Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching 基于超图极大匹配的确定性分布式边着色

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-10 DOI: 10.1109/FOCS.2017.25

Manuela Fischer, M. Ghaffari, F. Kuhn

{"title":"Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching","authors":"Manuela Fischer, M. Ghaffari, F. Kuhn","doi":"10.1109/FOCS.2017.25","DOIUrl":"https://doi.org/10.1109/FOCS.2017.25","url":null,"abstract":"We present a deterministic distributed algorithm that computes a (2δ-1)-edge-coloring, or even list-edge-coloring, in any n-node graph with maximum degree δ, in O(log^8 δ ⋅ log n) rounds. This answers one of the long-standing open questions of distributed graph algorithms} from the late 1980s, which asked for a polylogarithmic-time algorithm. See, e.g., Open Problem 4 in the Distributed Graph Coloring book of Barenboim and Elkin. The previous best round complexities were 2^{O(√{log n})} by Panconesi and Srinivasan [STOC92] and Õ(√{δ}) + O(log^* n) by Fraigniaud, Heinrich, and Kosowski [FOCS16]. A corollary of our deterministic list-edge-coloring also improves the randomized complexity of (2δ-1)-edge-coloring to poly(loglog n) rounds.The key technical ingredient is a deterministic distributed algorithm for hypergraph maximal matching, which we believe will be of interest beyond this result. In any hypergraph of rank r — where each hyperedge has at most r vertices — with n nodes and maximum degree δ, this algorithm computes a maximal matching in O(r^5 log^{6+log r } δ ⋅ log n) rounds.This hypergraph matching algorithm and its extensions also lead to a number of other results. In particular, we obtain a polylogarithmic-time deterministic distributed maximal independent set (MIS) algorithm for graphs with bounded neighborhood independence, hence answering Open Problem 5 of Barenboim and Elkins book, a big((log δ/ε)^{O(log 1/ε)}big)-round deterministic algorithm for (1+ε)-approximation of maximum matching, and a quasi-polylogarithmic-time deterministic distributed algorithm for orienting λ-arboricity graphs with out-degree at most lceil (1+ε)λ rceil, for any constant ε 0, hence partially answering Open Problem 10 of Barenboim and Elkins book.","PeriodicalId":311592,"journal":{"name":"2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129716551","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: 69

Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods 基于盒约束牛顿法和内点法的矩阵缩放和平衡

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-07 DOI: 10.1109/FOCS.2017.88

Michael B. Cohen, A. Madry, Dimitris Tsipras, Adrian Vladu

{"title":"Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods","authors":"Michael B. Cohen, A. Madry, Dimitris Tsipras, Adrian Vladu","doi":"10.1109/FOCS.2017.88","DOIUrl":"https://doi.org/10.1109/FOCS.2017.88","url":null,"abstract":"In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring logarithmic factors involving the dimension of the input matrix and the size of its entries, both run in time widetilde{O}(mlog kappa log^2 (1/≥ilon)) where ≥ilon is the amount of error we are willing to tolerate. Here, kappa represents the ratio between the largest and the smallest entries of the optimal scalings. This implies that our algorithms run in nearly-linear time whenever kappa is quasi-polynomial, which includes, in particular, the case of strictly positive matrices. We complement our results by providing a separate algorithm that uses an interior-point method and runs in time widetilde{O}(m^{3/2} log (1/≥ilon)).In order to establish these results, we develop a new second-order optimization framework that enables us to treat both problems in a unified and principled manner. This framework identifies a certain generalization of linear system solving that we can use to efficiently minimize a broad class of functions, which we call second-order robust. We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via this framework very efficient.","PeriodicalId":311592,"journal":{"name":"2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128138369","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: 109

Much Faster Algorithms for Matrix Scaling 更快的矩阵缩放算法

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-07 DOI: 10.1109/FOCS.2017.87

Zeyuan Allen-Zhu, Yuanzhi Li, R. Oliveira, A. Wigderson

引用次数: 105

Testing Hereditary Properties of Ordered Graphs and Matrices 检验有序图和矩阵的遗传性质

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-07 DOI: 10.1109/FOCS.2017.83

N. Alon, Omri Ben-Eliezer, E. Fischer

{"title":"Testing Hereditary Properties of Ordered Graphs and Matrices","authors":"N. Alon, Omri Ben-Eliezer, E. Fischer","doi":"10.1109/FOCS.2017.83","DOIUrl":"https://doi.org/10.1109/FOCS.2017.83","url":null,"abstract":"We consider properties of edge-colored vertex-ordered graphs} – graphs with a totally ordered vertex set and a finite set of possible edge colors – showing that any hereditary property of such graphs is strongly testable, i.e., testable with a constant number of queries. We also explain how the proof can be adapted to show that any hereditary property of two-dimensional matrices over a finite alphabet (where row and column order is not ignored) is strongly testable. The first result generalizes the result of Alon and Shapira [FOCS05; SICOMP08], who showed that any hereditary graph property (without vertex order) is strongly testable. The second result answers and generalizes a conjecture of Alon, Fischer and Newman [SICOMP07] concerning testing of matrix properties.The testability is proved by establishing a removal lemma for vertex-ordered graphs. It states that if such a graph is far enough from satisfying a certain hereditary property, then most of its induced vertex-ordered subgraphs on a certain (large enough) constant number of vertices do not satisfy the property as well.The proof bridges the gap between techniques related to the regularity lemma, used in the long chain of papers investigating graph testing, and string testing techniques. Along the way we develop a Ramsey-type lemma for multipartite graphs with undesirable edges, stating that one can find a Ramsey-type structure in such a graph, in which the density of the undesirable edges is not much higher than the density of those edges in the graph.","PeriodicalId":311592,"journal":{"name":"2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131297044","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

A Proof of CSP Dichotomy Conjecture CSP二分类猜想的一个证明

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-06 DOI: 10.1109/FOCS.2017.38

Dmitriy Zhuk

引用次数: 361

Optimal Las Vegas Locality Sensitive Data Structures 最佳拉斯维加斯位置敏感数据结构

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-06 DOI: 10.1109/FOCS.2017.91

Thomas Dybdahl Ahle

引用次数: 18

The Matching Problem in General Graphs Is in Quasi-NC 一般图的匹配问题属于准nc问题

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-06 DOI: 10.1109/FOCS.2017.70

O. Svensson, Jakub Tarnawski

引用次数: 50

Optimal Lower Bounds for Universal Relation, and for Samplers and Finding Duplicates in Streams 通用关系的最优下界，以及采样器和查找流中的重复项

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-04-03 DOI: 10.1109/FOCS.2017.50

M. Kapralov, Jelani Nelson, J. Pachocki, Zhengyu Wang, David P. Woodruff, Mobin Yahyazadeh

引用次数: 41

A Nearly Optimal Lower Bound on the Approximate Degree of AC^0 AC^0近似次的近最优下界

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-03-16 DOI: 10.1109/FOCS.2017.10

Mark Bun, J. Thaler

{"title":"A Nearly Optimal Lower Bound on the Approximate Degree of AC^0","authors":"Mark Bun, J. Thaler","doi":"10.1109/FOCS.2017.10","DOIUrl":"https://doi.org/10.1109/FOCS.2017.10","url":null,"abstract":"The approximate degree of a Boolean function f: {-1, 1}^n ↦ {-1, 1} is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. We introduce a generic method for increasing the approximate degree of a given function, while preserving its computability by constant-depth circuits.Specifically, we show how to transform any Boolean function f with approximate degree d into a function F on O(n polylog(n)) variables with approximate degree at least D = Ω(n^{1/3} d^{2/3}). In particular, if d = n^{1-Ω(1), then D is polynomially larger than d. Moreover, if f is computed by a constant-depth polynomial-size Boolean circuit, then so is F.By recursively applying our transformation, for any constant δ 0 we exhibit an AC° function of approximate degree Ω(n^{1-δ}). This improves over the best previous lower bound of Ω(n^{2/3}) due to Aaronson and Shi (J. ACM 2004), and nearly matches the trivial upper bound of n that holds for any function. Our lower bounds also apply to (quasipolynomial-size) DNFs of polylogarithmic width.We describe several applications of these results. We give:• For any constant δ 0, an Ω(n^{1-δ}) lower bound on the quantum communication complexity of a function in AC°.• A Boolean function f with approximate degree at least C(f)^{2-o(1), where C(f) is the certificate complexity of f. This separation is optimal up to the o(1) term in the exponent.• Improved secret sharing schemes with reconstruction procedures in AC°.","PeriodicalId":311592,"journal":{"name":"2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130168218","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: 33

A Dichotomy Theorem for Nonuniform CSPs 非一致csp的一个二分定理

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2017-03-08 DOI: 10.1109/FOCS.2017.37

A. Bulatov

引用次数: 365