SIAM journal on computing (Print)最新文献

{"title":"Computing the Discrete Fréchet Distance in Subquadratic Time","authors":"P. Agarwal, Rinat Ben Avraham, Haim Kaplan, M. Sharir","doi":"10.1137/130920526","DOIUrl":"https://doi.org/10.1137/130920526","url":null,"abstract":"The Frechet distance is a similarity measure between two curves A and B that takes into account the location and ordering of the points along the two curves: Informally, it is the minimum length of a leash required to connect a dog, walking along A, and its owner, walking along B, as they walk without backtracking along their respective curves from one endpoint to the other. \u0000 \u0000The discrete Frechet distance replaces the dog and its owner by a pair of frogs that can only reside on n and m specific stones on the curves A and B, respectively. These frogs hop from one stone to the next without backtracking, and the discrete Frechet distance is the minimum length of a \"leash\" that connects the frogs and allows them to execute such a sequence of hops. It can be computed in quadratic time by a straightforward dynamic programming algorithm. \u0000 \u0000We present the first subquadratic algorithm for computing the discrete Frechet distance between two sequences of points in the plane. Assuming m ≤ n, the algorithm runs in O(mn log log n/log n) time, in the standard RAM model, using O(n) storage. Our approach uses the geometry of the problem in a subtle way to encode legal positions of the frogs as states of a finite automaton.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130119632","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}

{"title":"Clustering under Perturbation Resilience","authors":"Maria-Florina Balcan, Yingyu Liang","doi":"10.1137/140981575","DOIUrl":"https://doi.org/10.1137/140981575","url":null,"abstract":"Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial [6] proposed analyzing objective based clustering problems under the assumption that the optimum clustering to the objective is preserved under small multiplicative perturbations to distances between points. In this paper, we provide several results within this framework. For separable center-based objectives, we present an algorithm that can optimally cluster instances resilient to $(1 + sqrt{2})$-factor perturbations, solving an open problem of Awasthi et al. [2]. For the k-median objective, we additionally give algorithms for a weaker, relaxed, and more realistic assumption in which we allow the optimal solution to change in a small fraction of the points after perturbation. We also provide positive results for min-sum clustering which is a generally much harder objective than k-median (and also non-center-based). Our algorithms are based on new linkage criteria that may be of independent interest.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126151091","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}

{"title":"On a Linear Program for Minimum-Weight Triangulation","authors":"A. Yousefi, N. Young","doi":"10.1137/120887928","DOIUrl":"https://doi.org/10.1137/120887928","url":null,"abstract":"Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial-time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122905098","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}

{"title":"Quantum Query Complexity of Minor-Closed Graph Properties","authors":"Andrew M. Childs, Robin Kothari","doi":"10.4230/LIPIcs.STACS.2011.661","DOIUrl":"https://doi.org/10.4230/LIPIcs.STACS.2011.661","url":null,"abstract":"We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties---those that cannot be characterized by a finite set of forbidden subgraphs---have quantum query complexity $Theta(n^{3/2})$. To establish this, we prove an adversary lower bound using a detailed analysis of the structure of minor-closed properties with respect to forbidden topological minors and forbidden subgraphs. On the other hand, we show that minor-closed properties (and more generally, sparse graph properties) that can be characterized by finitely many forbidden subgraphs can be solved strictly faster, in $o(n^{3/2})$ queries. Our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph-finding problems.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125421395","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}

{"title":"A Polynomial-Time Algorithm for Estimating the Partition Function of the Ferromagnetic Ising Model on a Regular Matroid","authors":"L. A. Goldberg, M. Jerrum","doi":"10.1137/110851213","DOIUrl":"https://doi.org/10.1137/110851213","url":null,"abstract":"We investigate the computational difficulty of approximating the partition function of the ferromagnetic Ising model on a regular matroid. Jerrum and Sinclair have shown that there is a fully polynomial randomised approximation scheme (FPRAS) for the class of graphic matroids. On the other hand, the authors have previously shown, subject to a complexity-theoretic assumption, that there is no FPRAS for the class of binary matroids, which is a proper superset of the class of graphic matroids. In order to map out the region where approximation is feasible, we focus on the class of regular matroids, an important class of matroids which properly includes the class of graphic matroids, and is properly included in the class of binary matroids. Using Seymour's decomposition theorem, we give an FPRAS for the class of regular matroids.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"229 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125783684","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}

{"title":"Optimal Cover of Points by Disks in a Simple Polygon","authors":"Haim Kaplan, M. J. Katz, G. Morgenstern, M. Sharir","doi":"10.1137/100808459","DOIUrl":"https://doi.org/10.1137/100808459","url":null,"abstract":"Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set O of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1968 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127460458","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}

{"title":"Determining Edge Expansion and Other Connectivity Measures of Graphs of Bounded Genus","authors":"V. Patel","doi":"10.1137/100811416","DOIUrl":"https://doi.org/10.1137/100811416","url":null,"abstract":"In this paper, we show that for an n-vertex graph G of genus g, the edge expansion of G can be determined in time nO(g2). We show that the same is true for various other similar measures of edge connectivity.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122241313","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}

{"title":"The Recognition of Tolerance and Bounded Tolerance Graphs","authors":"G. Mertzios, Ignasi Sau, S. Zaks","doi":"10.4230/LIPIcs.STACS.2010.2487","DOIUrl":"https://doi.org/10.4230/LIPIcs.STACS.2010.2487","url":null,"abstract":"Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its numerous applications (in bioinformatics, constraint-based temporal reasoning, resource allocation, and scheduling problems, among others). Several efficient algorithms for optimization problems that are NP-hard in general graphs have been designed for tolerance graphs. In spite of this, the recognition of tolerance graphs—namely, the problem of deciding whether a given graph is a tolerance graph—as well as the recognition of their main subclass of bounded tolerance graphs, have been the most fundamental open problems on this class of graphs (cf. the book on tolerance graphs [M. C. Golumbic and A. N. Trenk, Tolerance Graphs, Cambridge Stud. Adv. Math. 89, Cambridge University Press, Cambridge, UK, 2004]) since their introduction in 1982 [M. C. Golumbic and C. L. Monma, Proceedings of the 13th Southeastern Conference on Combinatorics, Graph Theory and Computing, Congr. Numer., 35 (1982), pp. 321-331]. In this article we prove that both recognition problems are NP-complete, even in the case where the input graph is a trapezoid graph. The presented results are surprising because, on the one hand, most subclasses of perfect graphs admit polynomial recognition algorithms and, on the other hand, bounded tolerance graphs were believed to be efficiently recognizable as they are a natural special case of trapezoid graphs (which can be recognized in polynomial time) and share a very similar structure with them. For our reduction we extend the notion of an acyclic orientation of permutation and trapezoid graphs. Our main tool is a new algorithm that uses vertex splitting to transform a given trapezoid graph into a permutation graph, while preserving this new acyclic orientation property. This method of vertex splitting is of independent interest; very recently, it was also proved a powerful tool in the design of efficient recognition algorithms for other classes of graphs [G. B. Mertzios and D. G. Corneil, Discrete Appl. Math., 159 (2011), pp. 1131-1147].","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125978180","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}

{"title":"Regular Expressions with Counting: Weak versus Strong Determinism","authors":"W. Gelade, M. Gyssens, W. Martens","doi":"10.1137/100814196","DOIUrl":"https://doi.org/10.1137/100814196","url":null,"abstract":"We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which almost coincide for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show that weakly deterministic expressions with counting are exponentially more succinct and strictly more expressive than strongly deterministic ones, even though they still do not capture all regular languages. In addition, we present a finite automaton model with counters, study its properties and investigate the natural extension of the Glushkov construction translating expressions with counting into such counting automata. This translation yields a deterministic automaton if and only if the expression is strongly deterministic. These results then also allow to derive upper bounds for decision problems for strongly deterministic expressions with counting.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127393833","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}

{"title":"Public-Key Cryptosystems Resilient to Key Leakage","authors":"M. Naor, G. Segev","doi":"10.1137/100813464","DOIUrl":"https://doi.org/10.1137/100813464","url":null,"abstract":"Most of the work in the analysis of cryptographic schemes is concentrated in abstract adversarial models that do not capture side-channel attacks. Such attacks exploit various forms of unintended i...","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125040024","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}