2010 IEEE 51st Annual Symposium on Foundations of Computer Science最新文献

The Monotone Complexity of k-clique on Random Graphs 随机图上k-团的单调复杂度

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/110839059

Benjamin Rossman

引用次数: 57

Local List Decoding with a Constant Number of Queries 使用常量查询数的本地列表解码

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.88

Avraham Ben-Aroya, K. Efremenko, A. Ta-Shma

引用次数: 34

The Sub-exponential Upper Bound for On-Line Chain Partitioning 联机链分区的次指数上界

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.40

B. Bosek, Tomasz Krawczyk

引用次数: 14

Learning Convex Concepts from Gaussian Distributions with PCA 用PCA从高斯分布中学习凸概念

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.19

S. Vempala

引用次数: 31

Replacement Paths via Fast Matrix Multiplication 替换路径通过快速矩阵乘法

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.68

O. Weimann, R. Yuster

{"title":"Replacement Paths via Fast Matrix Multiplication","authors":"O. Weimann, R. Yuster","doi":"10.1109/FOCS.2010.68","DOIUrl":"https://doi.org/10.1109/FOCS.2010.68","url":null,"abstract":"Let G be a directed edge-weighted graph and let P be a shortest path from s to t in G. The replacement paths problem asks to compute, for every edge e on P, the shortest s-to-t path that avoids e. Apart from approximation algorithms and algorithms for special graph classes, the naive solution to this problem – removing each edge e on P one at a time and computing the shortest s-to-t path each time – is surprisingly the only known solution for directed weighted graphs, even when the weights are integrals. In particular, although the related shortest paths problem has benefited from fast matrix multiplication, the replacement paths problem has not, and still required cubic time. For an n-vertex graph with integral edge-lengths between -M and M, we give a randomized algorithm that uses fast matrix multiplication and is sub-cubic for appropriate values of M. We also show how to construct a distance sensitivity oracle in the same time bounds. A query (u,v,e) to this oracle requires sub-quadratic time and returns the length of the shortest u-to-v path that avoids the edge e. In fact, for any constant number of edge failures, we construct a data structure in sub-cubic time, that answer queries in sub-quadratic time. Our results also apply for avoiding vertices rather than edges.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131091573","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: 26

Estimating the Longest Increasing Sequence in Polylogarithmic Time 多对数时间最长递增序列的估计

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/130942152

M. Saks, C. Seshadhri

{"title":"Estimating the Longest Increasing Sequence in Polylogarithmic Time","authors":"M. Saks, C. Seshadhri","doi":"10.1137/130942152","DOIUrl":"https://doi.org/10.1137/130942152","url":null,"abstract":"Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple O(n log n) time algorithms are known that determine the LIS exactly. In this paper, we develop a randomized approximation algorithm, that for any constant delta > 0, runs in time polylogarithmic in n and estimates the length of the LIS of an array up to an additive error of (delta n). The algorithm presented in this extended abstract runs in time (log n)^{O(1/delta)}. In the full paper, we will give an improved version of the algorithm with running time (log n)^c (1/delta)^{O(1/delta)} where the exponent c is independent of delta. Previously, the best known polylogarithmic time algorithms could only achieve an additive n/2-approximation. Our techniques also yield a fast algorithm for estimating the distance to monotonicity to within a small multiplicative factor. The distance of f to monotonicity, eps_f, is equal to 1 - |LIS|/n (the fractional length of the complement of the LIS). For any delta > 0, we give an algorithm with running time O((eps^{-1}_f log n)^{O(1/delta)}) that outputs a (1+delta)-multiplicative approximation to eps_f. This can be improved so that the exponent is a fixed constant. The previously known polylogarithmic algorithms gave only a 2-approximation.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132156299","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: 40

Testing Properties of Sparse Images 稀疏图像的性能测试

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1145/2635806

D. Ron, Gilad Tsur

引用次数: 18

The Coin Problem and Pseudorandomness for Branching Programs 分支规划的硬币问题与伪随机性

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.10

Joshua Brody, Elad Verbin

{"title":"The Coin Problem and Pseudorandomness for Branching Programs","authors":"Joshua Brody, Elad Verbin","doi":"10.1109/FOCS.2010.10","DOIUrl":"https://doi.org/10.1109/FOCS.2010.10","url":null,"abstract":"The emph{Coin Problem} is the following problem: a coin is given, which lands on head with probability either $1/2 + beta$ or $1/2 - beta$. We are given the outcome of $n$ independent tosses of this coin, and the goal is to guess which way the coin is biased, and to answer correctly with probability $ge 2/3$. When our computational model is unrestricted, the majority function is optimal, and succeeds when $beta ge c /sqrt{n}$ for a large enough constant $c$. The coin problem is open and interesting in models that cannot compute the majority function. In this paper we study the coin problem in the model of emph{read-once width-$w$ branching programs}. We prove that in order to succeed in this model, $beta$ must be at least $1/ (log n)^{Theta(w)}$. For constant $w$ this is tight by considering the recursive tribes function, and for other values of $w$ this is nearly tight by considering other read-once AND-OR trees. We generalize this to a emph{Dice Problem}, where instead of independent tosses of a coin we are given independent tosses of one of two $m$-sided dice. We prove that if the distributions are too close and the mass of each side of the dice is not too small, then the dice cannot be distinguished by small-width read-once branching programs. We suggest one application for this kind of theorems: we prove that Nisan's Generator fools width-$w$ read-once emph{regular} branching programs, using seed length $O(w^4 log n log log n + log n log (1/eps))$. For $w=eps=Theta(1)$, this seed length is $O(log n log log n)$. The coin theorem and its relatives might have other connections to PRGs. This application is related to the independent, but chronologically-earlier, work of Braver man, Rao, Raz and Yehudayoff~cite{BRRY}.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"1027 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116258373","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: 75

Subcubic Equivalences between Path, Matrix and Triangle Problems 路径、矩阵和三角形问题之间的次立方等价

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1145/3186893

V. V. Williams, Ryan Williams

{"title":"Subcubic Equivalences between Path, Matrix and Triangle Problems","authors":"V. V. Williams, Ryan Williams","doi":"10.1145/3186893","DOIUrl":"https://doi.org/10.1145/3186893","url":null,"abstract":"We say an algorithm on n by n matrices with entries in [-M, M] (or n-node graphs with edge weights from [-M, M]) is truly sub cubic if it runs in O(n^{3-delta} poly(log M)) time for some delta > 0. We define a notion of sub cubic reducibility, and show that many important problems on graphs and matrices solvable in O(n^3) time are equivalent under sub cubic reductions. Namely, the following weighted problems either all have truly sub cubic algorithms, or none of them do: - The all-pairs shortest paths problem (APSP). - Detecting if a weighted graph has a triangle of negative total edge weight. - Listing up to n^{2.99} negative triangles in an edge-weighted graph. - Finding a minimum weight cycle in a graph of non-negative edge weights. - The replacement paths problem in an edge-weighted digraph. - Finding the second shortest simple path between two nodes in an edge-weighted digraph. - Checking whether a given matrix defines a metric. - Verifying the correctness of a matrix product over the (min, +)-semiring. Therefore, if APSP cannot be solved in n^{3-eps} time for any eps > 0, then many other problems also need essentially cubic time. In fact we show generic equivalences between matrix products over a large class of algebraic structures used in optimization, verifying a matrix product over the same structure, and corresponding triangle detection problems over the structure. These equivalences simplify prior work on sub cubic algorithms for all-pairs path problems, since it now suffices to give appropriate sub cubic triangle detection algorithms. Other consequences of our work are new combinatorial approaches to Boolean matrix multiplication over the (OR, AND)-semiring (abbreviated as BMM). We show that practical advances in triangle detection would imply practical BMM algorithms, among other results. Building on our techniques, we give two new BMM algorithms: a derandomization of the recent combinatorial BMM algorithm of Bansal and Williams (FOCS'09), and an improved quantum algorithm for BMM.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133440712","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: 400

Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction 广义二次价格拍卖中无政府状态的纯粹价格和贝叶斯-纳什价格

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.75

R. Leme, É. Tardos

{"title":"Pure and Bayes-Nash Price of Anarchy for Generalized Second Price Auction","authors":"R. Leme, É. Tardos","doi":"10.1109/FOCS.2010.75","DOIUrl":"https://doi.org/10.1109/FOCS.2010.75","url":null,"abstract":"The Generalized Second Price Auction has been the main mechanism used by search companies to auction positions for advertisements on search pages. In this paper we study the social welfare of the Nash equilibria of this game in various models. In the full information setting, socially optimal Nash equilibria are known to exist (i.e., the Price of Stability is 1). This paper is the first to prove bounds on the price of anarchy, and to give any bounds in the Bayesian setting. Our main result is to show that the price of anarchy is small assuming that all bidders play un-dominated strategies. In the full information setting we prove a bound of 1.618 for the price of anarchy for pure Nash equilibria, and a bound of 4 for mixed Nash equilibria. We also prove a bound of 8 for the price of anarchy in the Bayesian setting, when valuations are drawn independently, and the valuation is known only to the bidder and only the distributions used are common knowledge. Our proof exhibits a combinatorial structure of Nash equilibria and uses this structure to bound the price of anarchy. While establishing the structure is simple in the case of pure and mixed Nash equilibria, the extension to the Bayesian setting requires the use of novel combinatorial techniques that can be of independent interest.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115971994","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: 115