2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)最新文献_第5页

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-06-28 DOI: 10.1109/FOCS.2016.23

Sungjin Im, Shi Li

{"title":"Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-uniform Distributions","authors":"Sungjin Im, Shi Li","doi":"10.1109/FOCS.2016.23","DOIUrl":"https://doi.org/10.1109/FOCS.2016.23","url":null,"abstract":"In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, R|rij| Σj wjCj using the three-field notation. For this problem, a 2-approximation is known based on a novel convex programming (J. ACM 2001 by Skutella). It has been a long standing open problem if one can improve upon this 2-approximation (Open Problem 8 in J. of Sched. 1999 by Schuurman and Woeginger). We answer this question in the affirmative by giving a 1.8786-approximation. We achieve this via a surprisingly simple linear programming, but a novel rounding algorithm and analysis. A key ingredient of our algorithm is the use of random offsets sampled from non-uniform distributions. We also consider the preemptive version of the problem, i.e, R|rij, pmtn|ΣjwjCj. We again use the idea of sampling offsets from non-uniform distributions to give the first better than 2-approximation for this problem. This improvement also requires use of a configuration LP with variables for each job's complete schedules along with more careful analysis. For both non-preemptive and preemptive versions, we break the approximation barrier of 2 for the first time.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131392742","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

Towards Strong Reverse Minkowski-Type Inequalities for Lattices 格的强逆minkowski型不等式

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-06-22 DOI: 10.1109/FOCS.2016.55

D. Dadush, O. Regev

引用次数: 19

Settling the Complexity of Computing Approximate Two-Player Nash Equilibria 求解近似二人纳什均衡的复杂度

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-06-14 DOI: 10.1145/3055589.3055596

A. Rubinstein

引用次数: 123

Hopsets with Constant Hopbound, and Applications to Approximate Shortest Paths 常希望界hopset及其在最短路径近似中的应用

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-05-15 DOI: 10.1109/FOCS.2016.22

Michael Elkin, Ofer Neiman

{"title":"Hopsets with Constant Hopbound, and Applications to Approximate Shortest Paths","authors":"Michael Elkin, Ofer Neiman","doi":"10.1109/FOCS.2016.22","DOIUrl":"https://doi.org/10.1109/FOCS.2016.22","url":null,"abstract":"A (β, ∈)-hopset for a weighted undirected n-vertex graph G = (V, E) is a set of edges, whose addition to the graph guarantees that every pair of vertices has a path between them that contains at most β edges, whose length is within 1 + ∈ of the shortest path. In her seminal paper, Cohen [8, JACM 2000] introduced the notion of hopsets in the context of parallel computation of approximate shortest paths, and since then it has found numerous applications in various other settings, such as dynamic graph algorithms, distributed computing, and the streaming model. Cohen [8] devised efficient algorithms for constructing hopsets with polylogarithmic in n number of hops. Her constructions remain the state-of-the-art since the publication of her paper in STOC'94, i.e., for more than two decades. In this paper we exhibit the first construction of sparse hopsets with a constant number of hops. We also find efficient algorithms for hopsets in various computational settings, improving the best known constructions. Generally, our hopsets strictly outperform the hopsets of [8], both in terms of their parameters, and in terms of the resources required to construct them. We demonstrate the applicability of our results for the fundamental problem of computing approximate shortest paths from s sources. Our results improve the running time for this problem in the parallel, distributed and streaming models, for a vast range of s.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121474791","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: 77

Popular Conjectures as a Barrier for Dynamic Planar Graph Algorithms 流行猜想是动态平面图算法的障碍

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-05-12 DOI: 10.1109/FOCS.2016.58

Amir Abboud, Søren Dahlgaard

{"title":"Popular Conjectures as a Barrier for Dynamic Planar Graph Algorithms","authors":"Amir Abboud, Søren Dahlgaard","doi":"10.1109/FOCS.2016.58","DOIUrl":"https://doi.org/10.1109/FOCS.2016.58","url":null,"abstract":"The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph G such that we may support insertions and deletions of edges in G as well as distance queries between any two nodes u, v subject to the constraint that the graph remains planar at all times. This problem has been extensively studied in both the theory and experimental communities over the past decades. The best known algorithm performs queries and updates in Õ(n2/3) time, based on ideas of a seminal paper by Fakcharoenphol and Rao [FOCS'01]. A (1+ε)-approximation algorithm of Abraham et al. [STOC'12] performs updates and queries in Õ(√n) time. An algorithm with a more practical O(polylog(n)) runtime would be a major breakthrough. However, such runtimes are only known for a (1+ε)-approximation in a model where only restricted weight updates are allowed due to Abraham et al. [SODA'16], or for easier problems like connectivity. In this paper, we follow a recent and very active line of work on showing lower bounds for polynomial time problems based on popular conjectures, obtaining the first such results for natural problems in planar graphs. Such results were previously out of reach due to the highly non-planar nature of known reductions and the impossibility of \"planarizing gadgets\". We introduce a new framework which is inspired by techniques from the literatures on distance labelling schemes and on parameterized complexity. Using our framework, we show that no algorithm for dynamic shortest paths or maximum weight bipartite matching in planar graphs can support both updates and queries in amortized O(n1/2-ε) time, for any ε>0, unless the classical all-pairs-shortest-paths problem can be solved in truly subcubic time, which is widely believed to be impossible. We extend these results to obtain strong lower bounds for other related problems as well as for possible trade-offs between query and update time. Interestingly, our lower bounds hold even in very restrictive models where only weight updates are allowed.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128508419","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: 68

An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound Komlós猜想匹配Banaszczyk界的算法

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-05-10 DOI: 10.1109/FOCS.2016.89

N. Bansal, D. Dadush, S. Garg

引用次数: 57

Approximate Gaussian Elimination for Laplacians - Fast, Sparse, and Simple 近似高斯消除拉普拉斯-快速，稀疏，简单

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-05-08 DOI: 10.1109/FOCS.2016.68

Rasmus Kyng, Sushant Sachdeva

引用次数: 164

Separations in Communication Complexity Using Cheat Sheets and Information Complexity 使用小抄表和信息复杂性分离通信复杂性

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-05-04 DOI: 10.1109/FOCS.2016.66

Anurag Anshu, Aleksandrs Belovs, S. Ben-David, Mika Göös, Rahul Jain, Robin Kothari, Troy Lee, M. Santha

{"title":"Separations in Communication Complexity Using Cheat Sheets and Information Complexity","authors":"Anurag Anshu, Aleksandrs Belovs, S. Ben-David, Mika Göös, Rahul Jain, Robin Kothari, Troy Lee, M. Santha","doi":"10.1109/FOCS.2016.66","DOIUrl":"https://doi.org/10.1109/FOCS.2016.66","url":null,"abstract":"While exponential separations are known between quantum and randomized communication complexity for partial functions (Raz, STOC 1999), the best known separation between these measures for a total function is quadratic, witnessed by the disjointness function. We give the first super-quadratic separation between quantum and randomized communication complexity for a total function, giving an example exhibiting a power 2.5 gap. We further present a 1.5 power separation between exact quantum and randomized communication complexity, improving on the previous ≈ 1.15 separation by Ambainis (STOC 2013). Finally, we present a nearly optimal quadratic separation between randomized communication complexity and the logarithm of the partition number, improving upon the previous best power 1.5 separation due to Goos, Jayram, Pitassi, and Watson. Our results are the communication analogues of separations in query complexity proved using the recent cheat sheet framework of Aaronson, Ben-David, and Kothari (STOC 2016). Our main technical results are randomized communication and information complexity lower bounds for a family of functions, called lookup functions, that generalize and port the cheat sheet framework to communication complexity.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124028656","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: 22

Fully Dynamic Maximal Matching in Constant Update Time 恒定更新时间下的全动态最大匹配

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-04-28 DOI: 10.1109/FOCS.2016.43

Shay Solomon

{"title":"Fully Dynamic Maximal Matching in Constant Update Time","authors":"Shay Solomon","doi":"10.1109/FOCS.2016.43","DOIUrl":"https://doi.org/10.1109/FOCS.2016.43","url":null,"abstract":"Baswana, Gupta and Sen [FOCS'11] showed that fully dynamic maximal matching can be maintained in general graphs with logarithmic amortized update time. More specifically, starting from an empty graph on n fixed vertices, they devised a randomized algorithm for maintaining maximal matching over any sequence of t edge insertions and deletions with a total runtime of O(t log n) in expectation and O(t log n + n log2 n) with high probability. Whether or not this runtime bound can be improved towards O(t) has remained an important open problem. Despite significant research efforts, this question has resisted numerous attempts at resolution even for basic graph families such as forests. In this paper, we resolve the question in the affirmative, by presenting a randomized algorithm for maintaining maximal matching in general graphs with constant amortized update time. The optimal runtime bound O(t) of our algorithm holds both in expectation and with high probability. As an immediate corollary, we can maintain 2-approximate vertex cover with constant amortized update time. This result is essentially the best one can hope for (under the unique games conjecture) in the context of dynamic approximate vertex cover, culminating a long line of research. Our algorithm builds on Baswana et al.'s algorithm, but is inherently different and arguably simpler. As an implication of our simplified approach, the space usage of our algorithm is linear in the (dynamic) graph size, while the space usage of Baswana et al.'s algorithm is always at least Ω(n log n). Finally, we present applications to approximate weighted matchings and to distributed networks.","PeriodicalId":414001,"journal":{"name":"2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)","volume":"CE-27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126544399","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: 124

Agnostic Estimation of Mean and Covariance 均值和协方差的不可知论估计

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-04-24 DOI: 10.1109/FOCS.2016.76

Kevin A. Lai, Anup B. Rao, S. Vempala

引用次数: 309