2011 IEEE 52nd Annual Symposium on Foundations of Computer Science最新文献_第7页

Efficient Computation of Approximate Pure Nash Equilibria in Congestion Games 拥挤对策中近似纯纳什均衡的有效计算

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-04-14 DOI: 10.1109/FOCS.2011.50

I. Caragiannis, A. Fanelli, N. Gravin, Alexander Skopalik

{"title":"Efficient Computation of Approximate Pure Nash Equilibria in Congestion Games","authors":"I. Caragiannis, A. Fanelli, N. Gravin, Alexander Skopalik","doi":"10.1109/FOCS.2011.50","DOIUrl":"https://doi.org/10.1109/FOCS.2011.50","url":null,"abstract":"Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes $O(1)$-approximate Nash equilibria in these games. In particular, for congestion games with linear latency functions, our algorithm computes $(2+epsilon)$-approximate pure Nash equilibria in time polynomial in the number of players, the number of resources and $1/epsilon$. It also applies to games with polynomial latency functions with constant maximum degree $d$; there, the approximation guarantee is $d^{O(d)}$. The algorithm essentially identifies a polynomially long sequence of best-response moves that lead to an approximate equilibrium, the existence of such short sequences is interesting in itself. These are the first positive algorithmic results for approximate equilibria in non-symmetric congestion games. We strengthen them further by proving that, for congestion games that deviate from our mild assumptions, computing $rho$-approximate equilibria is {sf PLS}-complete for any polynomial-time computable $rho$.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114440505","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: 54

A Parallel Approximation Algorithm for Positive Semidefinite Programming 正半定规划的并行逼近算法

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-04-13 DOI: 10.1109/FOCS.2011.25

Rahul Jain, Penghui Yao

引用次数: 39

A Small PRG for Polynomial Threshold Functions of Gaussians 高斯多项式阈值函数的小PRG

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-04-06 DOI: 10.1109/FOCS.2011.16

D. Kane

引用次数: 31

The Grothendieck Constant is Strictly Smaller than Krivine's Bound 格罗滕迪克常数严格小于克里文界

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-03-31 DOI: 10.1017/fmp.2013.4

M. Braverman, K. Makarychev, Yury Makarychev, A. Naor

引用次数: 88

3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General 3-SAT更快，更简单- PPSZ保持的唯一sat边界

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-03-10 DOI: 10.1137/120868177

Timon Hertli

引用次数: 108

Fully Dynamic Maximal Matching in O (log n) Update Time 在O (log n)更新时间内的完全动态最大匹配

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-03-06 DOI: 10.1137/130914140

Surender Baswana, Manoj Gupta, Sandeep Sen

{"title":"Fully Dynamic Maximal Matching in O (log n) Update Time","authors":"Surender Baswana, Manoj Gupta, Sandeep Sen","doi":"10.1137/130914140","DOIUrl":"https://doi.org/10.1137/130914140","url":null,"abstract":"We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our data structure is randomized that takes $O( log n)$ expected amortized time for each edge update where $n$ is the number of vertices in the graph. While there is a trivial $O(n)$ algorithm for edge update, the previous best known result for this problem was due to Ivkovi'c and Llyodcite{llyod}. For a graph with $n$ vertices and $m$ edges, they give an $O( {(n+ m)}^{0.7072})$ update time algorithm which is sub linear only for a sparse graph. %To the best of our knowledge this %is the first polylog update time for maximal matching that implies an % exponential improvement from the previous results. For the related problem of maximum matching, Onak and Rubinfeld cite{onak} designed a randomized data structure that achieves $O(log^2 n)$ expected amortized time for each update for maintaining a $c$-approximate maximum matching for some large constant $c$. In contrast, we can maintain a factor two approximate maximum matching in $O(log n )$ expected amortized time per update as a direct corollary of the maximal matching scheme. This in turn also implies a two approximate vertex cover maintenance scheme that takes $O(log n )$expected amortized time per update.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122125964","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: 149

Near Optimal Column-Based Matrix Reconstruction 接近最优的基于列的矩阵重构

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-03-04 DOI: 10.1137/12086755X

Christos Boutsidis, P. Drineas, M. Magdon-Ismail

引用次数: 244

Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time 单指数时间下树宽参数化连通性问题的求解

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-03-02 DOI: 10.1145/3506707

Marek Cygan, Jesper Nederlof, Marcin Pilipczuk, Michal Pilipczuk, J. M. M. Van Rooij, J. O. Wojtaszczyk

{"title":"Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time","authors":"Marek Cygan, Jesper Nederlof, Marcin Pilipczuk, Michal Pilipczuk, J. M. M. Van Rooij, J. O. Wojtaszczyk","doi":"10.1145/3506707","DOIUrl":"https://doi.org/10.1145/3506707","url":null,"abstract":"For the vast majority of local problems on graphs of small tree width (where by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c^tw |V|^O(1) time algorithms, where tw is the tree width of the input graph G = (V, E) and c is a constant. On the other hand, for problems with a global requirement (usually connectivity) the best -- known algorithms were naive dynamic programming schemes running in at least tw^tw time. We breach this gap by introducing a technique we named Cut&Count that allows to produce c^tw |V|^O(1) time Monte Carlo algorithms for most connectivity-type problems, including Hamiltonian Path, Steiner Tree, Feedback Vertex Set and Connected Dominating Set. These results have numerous consequences in various fields, like parameterized complexity, exact and approximate algorithms on planar and H-minor-free graphs and exact algorithms on graphs of bounded degree. The constant c in our algorithms is in all cases small, and in several cases we are able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. In contrast to the problems aiming to minimize the number of connected components that we solve using Cut&Count as mentioned above, we show that, assuming the Exponential Time Hypothesis, the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128753266","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: 317

Privacy Amplification and Non-malleable Extractors via Character Sums 基于字符和的隐私放大和非延展性提取器

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-02-26 DOI: 10.1137/120868414

Y. Dodis, Xin Li, T. Wooley, David Zuckerman

{"title":"Privacy Amplification and Non-malleable Extractors via Character Sums","authors":"Y. Dodis, Xin Li, T. Wooley, David Zuckerman","doi":"10.1137/120868414","DOIUrl":"https://doi.org/10.1137/120868414","url":null,"abstract":"In studying how to communicate over a public channel with an active adversary, Dodis and Wichs introduced the notion of a non-malleable extractor. A non-malleable extractor dramatically strengthens the notion of a strong extractor. A strong extractor takes two inputs, a weakly-random $x$ and a uniformly random seed $y$, and outputs a string which appears uniform, even given $y$. For a non-malleable extractor $nm$, the output $nm(x,y)$ should appear uniform given $y$ as well as $nm(x,adv(y))$, where $adv$ is an arbitrary function with $adv(y) neq y$. We show that an extractor introduced by Chor and Gold reich is non-malleable when the entropy rate is above half. It outputs a linear number of bits when the entropy rate is $1/2 + alpha$, for any $alpha>0$. Previously, no nontrivial parameters were known for any non-malleable extractor. To achieve a polynomial running time when outputting many bits, we rely on a widely-believed conjecture about the distribution of prime numbers in arithmetic progressions. Our analysis involves a character sum estimate, which may be of independent interest. Using our non-malleable extractor, we obtain protocols for ``privacy amplification & quot;: key agreement between two parties who share a weakly-random secret. Our protocols work in the presence of an active adversary with unlimited computational power, and have asymptotically optimal entropy loss. When the secret has entropy rate greater than $1/2$, the protocol follows from a result of Dodis and Wichs, and takes two rounds. When the secret has entropy rate $delta$ for any constant~$delta>0$, our new protocol takes a constant (polynomial in $1/delta$) number of rounds. Our protocols run in polynomial time under the above well-known conjecture about primes.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114489962","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: 72

A Nearly-m log n Time Solver for SDD Linear Systems SDD线性系统的近m log n时间解算器

2011 IEEE 52nd Annual Symposium on Foundations of Computer Science Pub Date : 2011-02-23 DOI: 10.1109/FOCS.2011.85

I. Koutis, G. Miller, Richard Peng

引用次数: 278