2010 IEEE 51st Annual Symposium on Foundations of Computer Science最新文献_第4页

Subexponential Algorithms for Unique Games and Related Problems 唯一对策及相关问题的次指数算法

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1145/2775105

Sanjeev Arora, B. Barak, David Steurer

{"title":"Subexponential Algorithms for Unique Games and Related Problems","authors":"Sanjeev Arora, B. Barak, David Steurer","doi":"10.1145/2775105","DOIUrl":"https://doi.org/10.1145/2775105","url":null,"abstract":"We give a sub exponential time approximation algorithm for the textsc{Unique Games} problem. The algorithms run in time that is exponential in an arbitrarily small polynomial of the input size, $n^{epsilon}$. The approximation guarantee depends on~$epsilon$, but not on the alphabet size or the number of variables. We also obtain a sub exponential algorithms with improved approximations for textsc{Small-Set Expansion} and textsc{Multicut}. For textsc{Max Cut}, textsc{Sparsest Cut}, and textsc{Vertex Cover}, we give sub exponential algorithms with improved approximations on some interesting subclasses of instances. Khot's Unique Games Conjecture (UGC) states that it is NP-hard to achieve approximation guarantees such as ours for the textsc{Unique Games}. While our results stop short of refuting the UGC, they do suggest that textsc{Unique Games} is significantly easier than NP-hard problems such as textsc{Max 3Sat}, textsc{Max 3Lin}, textsc{Label Cover} and more, that are believed not to have a sub exponential algorithm achieving a non-trivial approximation ratio. The main component in our algorithms is a new result on graph decomposition that may have other applications. Namely we show that for every $epsilon>0$ and every regular $n$-vertex graph~$G$, by changing at most $epsilon$ fraction of $G$'s edges, one can break~$G$ into disjoint parts so that the stochastic adjacency matrix of the induced graph on each part has at most $ n^{epsilon}$ eigenvalues larger than $1-eta$, where $eta$ depends polynomially on $epsilon$.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"13 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":"128529056","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: 263

Minimum-Cost Network Design with (Dis)economies of Scale 具有(非)规模经济的最小成本网络设计

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/110825959

M. Andrews, S. Antonakopoulos, Lisa Zhang

{"title":"Minimum-Cost Network Design with (Dis)economies of Scale","authors":"M. Andrews, S. Antonakopoulos, Lisa Zhang","doi":"10.1137/110825959","DOIUrl":"https://doi.org/10.1137/110825959","url":null,"abstract":"Given a network, a set of demands and a cost function f(.), the min-cost network design problem is to route all demands with the objective of minimizing sum_e f(l_e), where l_e is the total traffic load under the routing. We focus on cost functions of the form f(x) = s + x^a for x &gt, 0, with f(0) = 0. For a 1 with a positive startup cost s &gt, 0. Now, the cost function f(.) is neither sub additive nor super additive. This is motivated by minimizing network-wide energy consumption when supporting a set of traffic demands. It is commonly accepted that, for some computing and communication devices, doubling processing speed more than doubles the energy consumption. Hence, in Economics parlance, such a cost function reflects diseconomies of scale. We begin by discussing why existing routing techniques such as randomized rounding and tree-metric embedding fail to generalize directly. We then present our main contribution, which is a polylogarithmic approximation algorithm. We obtain this result by first deriving a bicriteria approximation for a related capacitated min-cost flow problem that we believe is interesting in its own right. Our approach for this problem builds upon the well-linked decomposition due to Chekuri-Khanna-Shepherd, the construction of expanders via matchings due to Khandekar-Rao-Vazirani, and edge-disjoint routing in well-connected graphs due to Rao-Zhou. However, we also develop new techniques that allow us to keep a handle on the total cost, which was not a concern in the aforementioned literature.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"107 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":"127893744","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: 50

Deciding First-Order Properties for Sparse Graphs 确定稀疏图的一阶性质

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.20

Z. Dvořák, D. Král, R. Thomas

{"title":"Deciding First-Order Properties for Sparse Graphs","authors":"Z. Dvořák, D. Král, R. Thomas","doi":"10.1109/FOCS.2010.20","DOIUrl":"https://doi.org/10.1109/FOCS.2010.20","url":null,"abstract":"We present a linear-time algorithm for deciding first-order logic (FOL) properties in classes of graphs with bounded expansion. Many natural classes of graphs have bounded expansion: graphs of bounded tree-width, all proper minor-closed classes of graphs, graphs of bounded degree, graphs with no sub graph isomorphic to a subdivision of a fixed graph, and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges. We also develop an almost linear-time algorithm for deciding FOL properties in classes of graphs with locally bounded expansion, those include classes of graphs with locally bounded tree-width or locally excluding a minor. More generally, we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion. After a linear-time initialization the data structure allows us to test an FOL property in constant time, and the data structure can be updated in constant time after addition/deletion of an edge, provided the list of possible edges to be added is known in advance and their addition results in a graph in the class. In addition, we design a dynamic data structure for testing existential properties or the existence of short paths between prescribed vertices in such classes of graphs. All our results also hold for relational structures and are based on the seminal result of Nesetril and Ossona de Mendez on the existence of low tree-depth colorings.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"28 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":"122194548","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: 104

Pseudorandom Generators for Regular Branching Programs 正则分支程序的伪随机生成器

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/120875673

M. Braverman, Anup Rao, R. Raz, A. Yehudayoff

引用次数: 80

Cryptography against Continuous Memory Attacks 针对连续内存攻击的密码学

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.56

Y. Dodis, Kristiyan Haralambiev, Adriana López-Alt, D. Wichs

{"title":"Cryptography against Continuous Memory Attacks","authors":"Y. Dodis, Kristiyan Haralambiev, Adriana López-Alt, D. Wichs","doi":"10.1109/FOCS.2010.56","DOIUrl":"https://doi.org/10.1109/FOCS.2010.56","url":null,"abstract":"We say that a cryptographic scheme is Continuous Leakage-Resilient (CLR), if it allows users to refresh their secret keys, using only fresh local randomness, such that: 1. The scheme remains functional after any number of key refreshes, although the public key never changes. Thus, the “outside world'' is neither affected by these key refreshes, nor needs to know about their frequency. 2. The scheme remains secure even if the adversary can continuously leak arbitrary information about the current secret-key, as long as the amount of leaked information is bounded in between any two successive key refreshes. There is no bound on the total amount of information that can be leaked during the lifetime of the system. In this work, we construct a variety of practical CLR schemes, including CLR one-way relations, CLR signatures, CLR identification schemes, and CLR authenticated key agreement protocols. For each of the above, we give general constructions, and then show how to instantiate them efficiently using a well established assumption on bilinear groups, called the K-Linear assumption (for any constant K greater than or equal to 1). Our constructions are highly modular, and we develop many interesting techniques and building-blocks along the way, including: leakage-indistinguishable re-randomizable relations, homomorphic NIZKs, and leakage-of-cipher text non-malleable encryption schemes.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"37 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":"133326547","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: 218

A Unified Framework for Testing Linear-Invariant Properties 检验线性不变性质的统一框架

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1002/rsa.20507

Arnab Bhattacharyya, Elena Grigorescu, A. Shapira

{"title":"A Unified Framework for Testing Linear-Invariant Properties","authors":"Arnab Bhattacharyya, Elena Grigorescu, A. Shapira","doi":"10.1002/rsa.20507","DOIUrl":"https://doi.org/10.1002/rsa.20507","url":null,"abstract":"There has been a sequence of recent papers devoted to understanding the relation between the testability of properties of Boolean functions and the invariance of the properties with respect to transformations of the domain. Invariance with respect to F_2-linear transformations is arguably the most common such symmetry for natural properties of Boolean functions on the hypercube. Hence, it is an important goal to find necessary and sufficient conditions for testability of linear-invariant properties. This is explicitly posed as an open problem in a recent survey of Sudan. We obtain the following results: 1. We show that every linear-invariant property that can be characterized by forbidding induced solutions to a (possibly infinite) set of linear equations can be tested with one-sided error. 2. We show that every linear-invariant property that can be tested with one-sided error can be characterized by forbidding induced solutions to a (possibly infinite) set of {em systems} of linear equations. We conjecture that our result from item (1) can be extended to cover systems of linear equations. We further show that the validity of this conjecture would have the following implications: 1. It would imply that every linear-invariant property that is closed under restrictions to linear subspaces is testable with one-sided error. Such a result would unify several previous results on testing Boolean functions, such as the testability of low-degree polynomials and of Fourier dimensionality. 2. It would imply that a linear-invariant property ${cal P}$ is testable with one-sided error {bf if and only if} ${cal P}$ is closed under restrictions to linear subspaces, thus resolving Sudan's problem.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"63 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":"133565976","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: 55

Boosting and Differential Privacy 增强和区分隐私

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.12

C. Dwork, G. Rothblum, S. Vadhan

{"title":"Boosting and Differential Privacy","authors":"C. Dwork, G. Rothblum, S. Vadhan","doi":"10.1109/FOCS.2010.12","DOIUrl":"https://doi.org/10.1109/FOCS.2010.12","url":null,"abstract":"Boosting is a general method for improving the accuracy of learning algorithms. We use boosting to construct improved {em privacy-preserving synopses} of an input database. These are data structures that yield, for a given set $Q$ of queries over an input database, reasonably accurate estimates of the responses to every query in~$Q$, even when the number of queries is much larger than the number of rows in the database. Given a {em base synopsis generator} that takes a distribution on $Q$ and produces a ``weak'' synopsis that yields ``good'' answers for a majority of the weight in $Q$, our {em Boosting for Queries} algorithm obtains a synopsis that is good for all of~$Q$. We ensure privacy for the rows of the database, but the boosting is performed on the {em queries}. We also provide the first synopsis generators for arbitrary sets of arbitrary low-sensitivity queries, {it i.e.}, queries whose answers do not vary much under the addition or deletion of a single row. In the execution of our algorithm certain tasks, each incurring some privacy loss, are performed many times. To analyze the cumulative privacy loss, we obtain an $O(eps^2)$ bound on the {em expected} privacy loss from a single $eps$-dfp{} mechanism. Combining this with evolution of confidence arguments from the literature, we get stronger bounds on the expected cumulative privacy loss due to multiple mechanisms, each of which provides $eps$-differential privacy or one of its relaxations, and each of which operates on (potentially) different, adaptively chosen, databases.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"13 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":"122246253","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: 866

Adaptive Hardness and Composable Security in the Plain Model from Standard Assumptions 基于标准假设的平面模型的自适应硬度和组合安全性

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/110847196

R. Canetti, Huijia Lin, R. Pass

{"title":"Adaptive Hardness and Composable Security in the Plain Model from Standard Assumptions","authors":"R. Canetti, Huijia Lin, R. Pass","doi":"10.1137/110847196","DOIUrl":"https://doi.org/10.1137/110847196","url":null,"abstract":"We construct the first general secure computation protocols that require no trusted infrastructure other than authenticated communication, and that satisfy a meaningful notion of security that is preserved under universal composition—{em assuming only the existence of enhanced trapdoor permutations.} The notion of security fits within a generalization of the ``angel-based'' framework of Prabhakaran and Sahai (STOC'04) and implies super-polynomial time simulation security. Security notions of this kind are currently known to be realizable only under strong and specific hardness assumptions. A key element in our construction is a commitment scheme that satisfies a new and strong notion of security. The notion, security against chosen-commitment-attacks (CCA security), means that security holds even if the attacker has access to a {em extraction oracle} that gives the adversary decommitment information to commitments of the adversary's choice. This notion is stronger than concurrent non-malleability and is of independent interest. We construct CCA-secure commitments based on standard one-way functions, and with no trusted set-up. To the best of our knowledge, this provides the first construction of a natural cryptographic primitive requiring emph{adaptive hardness} from standard hardness assumptions, using no trusted set-up or public keys.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"112 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":"123594941","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: 93

Corrigendum: A Random Sampling Algorithm for Learning an Intersection of Halfspaces 更正:用于学习半空间交集的随机抽样算法

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.18

S. Vempala

引用次数: 0

Sublinear Optimization for Machine Learning 机器学习的次线性优化

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-21 DOI: 10.1145/2371656.2371658

K. Clarkson, Elad Hazan, David P. Woodruff

引用次数: 128