Proceedings of the forty-sixth annual ACM symposium on Theory of computing最新文献_第9页

Polynomial bounds for the grid-minor theorem 网格小定理的多项式界

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-28 DOI: 10.1145/2591796.2591813

C. Chekuri, Julia Chuzhoy

引用次数: 120

A characterization of strong approximation resistance 强逼近阻力的表征

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-23 DOI: 10.1145/2591796.2591817

Subhash Khot, Madhur Tulsiani, Pratik Worah

{"title":"A characterization of strong approximation resistance","authors":"Subhash Khot, Madhur Tulsiani, Pratik Worah","doi":"10.1145/2591796.2591817","DOIUrl":"https://doi.org/10.1145/2591796.2591817","url":null,"abstract":"For a predicate f: {-1, 1}k ↦ {0, 1} with ρ(f) = |f-1(1)|/2k, we call the predicate strongly approximation resistant if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment such that the fraction of constraints satisfied is outside the range [ρ(f) - Ω(1), ρ(f) + Ω(1)]. We present a characterization of strongly approximation resistant predicates under the Unique Games Conjecture. We also present characterizations in the mixed linear and semi-definite programming hierarchy and the Sherali-Adams linear programming hierarchy. In the former case, the characterization coincides with the one based on UGC. Each of the two characterizations is in terms of existence of a probability measure on a natural convex polytope associated with the predicate. The predicate is called approximation resistant if given a near-satisfiable instance of CSP(f), it is computationally hard to find an assignment such that the fraction of constraints satisfied is at least ρ(f) + Ω(1). When the predicate is odd, i.e. f(-z) = 1 - f(z), ∀z ∈ {-1, 1}k, it is easily observed that the notion of approximation resistance coincides with that of strong approximation resistance. Hence for odd predicates our characterization of strong approximation resistance is also a characterization of approximation resistance.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123370491","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: 27

Approximate distance oracles with constant query time 具有恒定查询时间的近似距离oracle

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-14 DOI: 10.1145/2591796.2591801

S. Chechik

引用次数: 71

Efficient density estimation via piecewise polynomial approximation 通过分段多项式近似的高效密度估计

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-14 DOI: 10.1145/2591796.2591848

Siu On Chan, Ilias Diakonikolas, R. Servedio, Xiaorui Sun

{"title":"Efficient density estimation via piecewise polynomial approximation","authors":"Siu On Chan, Ilias Diakonikolas, R. Servedio, Xiaorui Sun","doi":"10.1145/2591796.2591848","DOIUrl":"https://doi.org/10.1145/2591796.2591848","url":null,"abstract":"We give a computationally efficient semi-agnostic algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let p be an arbitrary distribution over an interval I, and suppose that p is τ-close (in total variation distance) to an unknown probability distribution q that is defined by an unknown partition of I into t intervals and t unknown degree d polynomials specifying q over each of the intervals. We give an algorithm that draws Õ(t(d + 1)/ε2) samples from p, runs in time poly(t, d + 1, 1/ε), and with high probability outputs a piecewise polynomial hypothesis distribution h that is (14τ + ε)-close to p in total variation distance. Our algorithm combines tools from real approximation theory, uniform convergence, linear programming, and dynamic programming. Its sample complexity is simultaneously near optimal in all three parameters t, d and ε; we show that even for τ = 0, any algorithm that learns an unknown t-piecewise degree-d probability distribution over I to accuracy ε must use [EQUATION] samples from the distribution, regardless of its running time. We apply this general algorithm to obtain a wide range of results for many natural density estimation problems over both continuous and discrete domains. These include state-of-the-art results for learning mixtures of log-concave distributions; mixtures of t-modal distributions; mixtures of Monotone Hazard Rate distributions; mixtures of Poisson Binomial Distributions; mixtures of Gaussians; and mixtures of k-monotone densities. Our general technique gives improved results, with provably optimal sample complexities (up to logarithmic factors) in all parameters in most cases, for all these problems via a single unified algorithm.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129654499","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: 117

Inapproximability for antiferromagnetic spin systems in the tree non-uniqueness region 树非唯一性区域中反铁磁自旋系统的不逼近性

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-13 DOI: 10.1145/2591796.2591878

Andreas Galanis, Daniel Stefankovic, Eric Vigoda

{"title":"Inapproximability for antiferromagnetic spin systems in the tree non-uniqueness region","authors":"Andreas Galanis, Daniel Stefankovic, Eric Vigoda","doi":"10.1145/2591796.2591878","DOIUrl":"https://doi.org/10.1145/2591796.2591878","url":null,"abstract":"A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree Δ undergoes a phase transition that coincides with the statistical physics uniqueness/non-uniqueness phase transition on the infinite Δ-regular tree. Despite this clear picture for 2-spin systems, there is little known for multi-spin systems. We present the first analog of the above inapproximability results for multi-spin systems. The main difficulty in previous inapproximability results was analyzing the behavior of the model on random Δ-regular bipartite graphs, which served as the gadget in the reduction. To this end one needs to understand the moments of the partition function. Our key contribution is connecting: (i) induced matrix norms, (ii) maxima of the expectation of the partition function, and (iii) attractive fixed points of the associated tree recursions (belief propagation). The view through matrix norms allows a simple and generic analysis of the second moment for any spin system on random Δ-regular bipartite graphs. This yields concentration results for any spin system in which one can analyze the maxima of the first moment. The connection to fixed points of the tree recursions enables an analysis of the maxima of the first moment for specific models of interest. For k-colorings we prove that for even k, in the tree non-uniqueness region (specifically for semi-translation invariant measures which corresponds to k < Δ) it is NP-hard, unless NP=RP, to approximate the number of colorings for triangle-free Δ-regular graphs. Our proof extends to the antiferromagnetic Potts model, and, in fact, to every antiferromagnetic model under a mild condition.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115938721","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: 34

Analytical approach to parallel repetition 平行重复的分析方法

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-05-08 DOI: 10.1145/2591796.2591884

Irit Dinur, David Steurer

{"title":"Analytical approach to parallel repetition","authors":"Irit Dinur, David Steurer","doi":"10.1145/2591796.2591884","DOIUrl":"https://doi.org/10.1145/2591796.2591884","url":null,"abstract":"We propose an analytical framework for studying parallel repetition, a basic product operation for one-round twoplayer games. In this framework, we consider a relaxation of the value of projection games. We show that this relaxation is multiplicative with respect to parallel repetition and that it provides a good approximation to the game value. Based on this relaxation, we prove the following improved parallel repetition bound: For every projection game G with value at most ρ, the k-fold parallel repetition G⊗k has value at most [EQUATION] This statement implies a parallel repetition bound for projection games with low value ρ. Previously, it was not known whether parallel repetition decreases the value of such games. This result allows us to show that approximating set cover to within factor (1 --- ε) ln n is NP-hard for every ε > 0, strengthening Feige's quasi-NP-hardness and also building on previous work by Moshkovitz and Raz. In this framework, we also show improved bounds for few parallel repetitions of projection games, showing that Raz's counterexample to strong parallel repetition is tight even for a small number of repetitions. Finally, we also give a short proof for the NP-hardness of label cover(1, δ) for all δ > 0, starting from the basic PCP theorem.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115470745","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: 441

Entropy, optimization and counting 熵，优化和计数

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-04-30 DOI: 10.1145/2591796.2591803

Mohit Singh, Nisheeth K. Vishnoi

{"title":"Entropy, optimization and counting","authors":"Mohit Singh, Nisheeth K. Vishnoi","doi":"10.1145/2591796.2591803","DOIUrl":"https://doi.org/10.1145/2591796.2591803","url":null,"abstract":"We study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. There has been a tremendous amount of interest in such distributions due to their applicability in areas such as statistical physics, economics, biology, information theory, machine learning, combinatorics and algorithms. However, a rigorous and systematic study of how to compute such distributions has been lacking. Since the underlying set of discrete objects can be exponential in the input size, the first question in such a study is if max-entropy distributions have polynomially-sized descriptions. We start by giving a structural result which shows that such succinct descriptions exist under very general conditions. Subsequently, we use techniques from convex programming to give a meta-algorithm that can efficiently (approximately) compute max-entropy distributions provided one can efficiently (approximately) count the underlying discrete set. Thus, we can translate a host of existing counting algorithms, developed in an unrelated context, into algorithms that compute max-entropy distributions. Conversely, we prove that counting oracles are necessary for computing max-entropy distributions: we show how algorithms that compute max-entropy distributions can be converted into counting algorithms.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131133375","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: 79

From hierarchical partitions to hierarchical covers: optimal fault-tolerant spanners for doubling metrics 从分层分区到分层覆盖:用于加倍度量的最佳容错扳手

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-04-30 DOI: 10.1145/2591796.2591864

Shay Solomon

{"title":"From hierarchical partitions to hierarchical covers: optimal fault-tolerant spanners for doubling metrics","authors":"Shay Solomon","doi":"10.1145/2591796.2591864","DOIUrl":"https://doi.org/10.1145/2591796.2591864","url":null,"abstract":"A (1+ε)-spanner for a doubling metric (X, δ) is a subgraph H of the complete graph corresponding to (X, δ), which preserves all pairwise distances to within a factor of 1 + ε. A natural requirement from a spanner, which is essential for many applications (mainly in distributed systems or wireless networks), is to be robust against vertex and edge failures -- so that even when some vertices and edges in the network fail, we still have a (1 + ε)-spanner for what remains. The spanner H is called a k-fault-tolerant (1 + ε)-spanner, for 1 ≤ k ≤ n -- 2, if for any F ⊆ X with |F| ≤ k, the graph H -- F (obtained by removing from H the vertices of F and their incident edges) is a (1 + ε)-spanner for X -- F. In this paper we devise an optimal construction of fault-tolerant spanners for doubling metrics: For any n-point doubling metric, any ε > 0, and any integer 1 ≤ k ≤ n -- 2, our construction provides a k-fault-tolerant (1+ε)-spanner with optimal degree O(k) within optimal time O(n log n + kn). We then strengthen this result to provide near-optimal (up to a factor of log k) guarantees on the diameter and weight of our spanners, namely, diameter O(log n) and weight O(k2 + k log n) · ω(MST), while preserving the optimal guarantees on the degree O(k) and the runtime O(n log n + kn). Our result settles several fundamental open questions in this area, culminating a long line of research that started with the STOC'95 paper of Arya et al. and the STOC'98 paper of Levcopoulos et al. On the way to this result we develop a new technique for constructing spanners in doubling metrics. In particular, our spanner construction is based on a novel hierarchical cover of the metric, whereas most previous constructions of spanners for doubling and Euclidean metrics (such as the net-tree spanner) are based on hierarchical partitions of the metric. We demonstrate the power of hierarchical covers in the context of geometric spanners by improving the state-of-the-art results in this area.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132531138","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: 35

Distributed computability in Byzantine asynchronous systems 拜占庭异步系统中的分布式可计算性

Proceedings of the forty-sixth annual ACM symposium on Theory of computing Pub Date : 2013-02-25 DOI: 10.1145/2591796.2591853

H. Mendes, C. Tasson, M. Herlihy

引用次数: 23