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

Adjacency Labeling Schemes and Induced-Universal Graphs 邻接标记方案与诱导泛图

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-04-13 DOI: 10.1145/2746539.2746545

Stephen Alstrup, Haim Kaplan, M. Thorup, Uri Zwick

引用次数: 56

A Directed Isoperimetric Inequality with application to Bregman Near Neighbor Lower Bounds 一个有向等周不等式及其在Bregman近邻下界上的应用

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-04-04 DOI: 10.1145/2746539.2746595

A. Abdullah, Suresh Venkatasubramanian

{"title":"A Directed Isoperimetric Inequality with application to Bregman Near Neighbor Lower Bounds","authors":"A. Abdullah, Suresh Venkatasubramanian","doi":"10.1145/2746539.2746595","DOIUrl":"https://doi.org/10.1145/2746539.2746595","url":null,"abstract":"Bregman divergences are important distance measures that are used in applications such as computer vision, text mining, and speech processing, and are a focus of interest in machine learning due to their information-theoretic properties. There has been extensive study of algorithms for clustering and near neighbor search with respect to these divergences. In all cases, the guarantees depend not just on the data size n and dimensionality d, but also on a structure constant μ ≥ 1 that depends solely on a generating convex function φ and can grow without bound independently. In general, this μ parametrizes the degree to which a given divergence is \"asymmetric\". In this paper, we provide the first evidence that this dependence on μ might be intrinsic. We focus on the problem of ac{ann} search for Bregman divergences. We show that under the cell probe model, any non-adaptive data structure (like locality-sensitive hashing) for c-approximate near-neighbor search that admits r probes must use space Ω(dn1 + μ/c r). In contrast for LSH under l1 the best bound is Ω(dn1+ 1/cr). Our results interpolate between known lower bounds both for LSH-based ANN under l1 as well as the generally harder Partial Match problem (in non-adaptive settings). The bounds match the former when μ is small and the latter when μ is Ω(d/log n). This further strengthens the intuition that Partial Match corresponds to an \"asymmetric\" version of ANN, as well as opening up the possibility of a new line of attack for lower bounds on Partial Match. Our new tool is a directed variant of the standard boolean noise operator. We prove a generalization of the Bonami-Beckner hypercontractivity inequality (restricted to certain subsets of the Hamming cube), and use this to prove the desired directed isoperimetric inequality that we use in our data structure lower bound.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77238581","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

Minimizing Flow-Time on Unrelated Machines 最小化不相关机器的流程时间

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2014-01-28 DOI: 10.1145/2746539.2746601

N. Bansal, Janardhan Kulkarni

引用次数: 21

On the Complexity of Random Satisfiability Problems with Planted Solutions 带种植解的随机可满足问题的复杂性

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2013-11-19 DOI: 10.1145/2746539.2746577

Vitaly Feldman, Will Perkins, S. Vempala

{"title":"On the Complexity of Random Satisfiability Problems with Planted Solutions","authors":"Vitaly Feldman, Will Perkins, S. Vempala","doi":"10.1145/2746539.2746577","DOIUrl":"https://doi.org/10.1145/2746539.2746577","url":null,"abstract":"The problem of identifying a planted assignment given a random k-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution can always be identified given a formula with O(n log n) clauses, there are distributions over clauses for which the best known efficient algorithms require nk/2 clauses. We propose and study a unified model for planted k-SAT, which captures well-known special cases. An instance is described by a planted assignment σ and a distribution on clauses with k literals. We define its distribution complexity as the largest r for which the distribution is not r-wise independent (1 ≤ r ≤ k for any distribution with a planted assignment). Our main result is an unconditional lower bound, tight up to logarithmic factors, of Ω(nr/2) clauses for statistical algorithms, matching the known upper bound (which, as we show, can be implemented using a statistical algorithm). Since known approaches for problems over distributions have statistical analogues (spectral, MCMC, gradient-based, convex optimization etc.), this lower bound provides a rigorous explanation of the observed algorithmic gap. The proof introduces a new general technique for the analysis of statistical algorithms. It also points to a geometric paring phenomenon in the space of all planted assignments. We describe consequences of our lower bounds to Feige's refutation hypothesis and to lower bounds on general convex programs that solve planted k-SAT. Our bounds also extend to the planted k-CSP model, defined by Goldreich as a candidate for one-way function, and therefore provide concrete evidence for the security of Goldreich's one-way function and the associated pseudorandom generator when used with a sufficiently hard predicate.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82688796","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

The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree 动态距离预言器的力量:斯坦纳树的有效动态算法

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2013-08-15 DOI: 10.1145/2746539.2746615

Jakub Lacki, Jakub Ocwieja, Marcin Pilipczuk, P. Sankowski, Anna Zych

{"title":"The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree","authors":"Jakub Lacki, Jakub Ocwieja, Marcin Pilipczuk, P. Sankowski, Anna Zych","doi":"10.1145/2746539.2746615","DOIUrl":"https://doi.org/10.1145/2746539.2746615","url":null,"abstract":"In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an n-vertex graph G=(V,E,w) with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set S ⊆ V, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear o(n) time, and keep the approximation factor of the algorithm as small as possible. We show that we can maintain a (6+ε)-approximate Steiner tree of a general graph in ~O(√n log D) time per terminal addition or removal. Here, strecz denotes the stretch of the metric induced by G. For planar graphs we achieve the same running time and the approximation ratio of (2+ε). Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time (4+ε)-approximate algorithm for planar graphs. One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84718122","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: 43

Sum-of-squares Lower Bounds for Planted Clique 植团的平方和下界

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 2013-07-01 DOI: 10.1145/2746539.2746600

R. Meka, Aaron Potechin, A. Wigderson

{"title":"Sum-of-squares Lower Bounds for Planted Clique","authors":"R. Meka, Aaron Potechin, A. Wigderson","doi":"10.1145/2746539.2746600","DOIUrl":"https://doi.org/10.1145/2746539.2746600","url":null,"abstract":"Finding cliques in random graphs and the closely related \"planted\" clique variant, where a clique of size k is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k = Θ(√n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-Of-Squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k ≥ (√n/log n)1/rCr. Thus, for any constant number of rounds planted cliques of size no(1) cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural \"dual certificate\" (also known as a \"vector-solution\" or \"pseudo-expectation\") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76420996","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

A combinatorial problem which is complete in polynomial space 一个在多项式空间中完备的组合问题

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803754

S. Even, R. Tarjan

引用次数: 33

Optimal code generation for expression trees 表达式树的最佳代码生成

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803770

A. Aho, Stephen C. Johnson

引用次数: 148

Computability concepts for programming language semantics 编程语言语义的可计算性概念

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803757

H. Egli, R. Constable

引用次数: 57

The optimal fixedpoint of recursive programs 递归程序的最优不动点

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803769

Z. Manna, A. Shamir

引用次数: 11