Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing最新文献

{"title":"Separator based sparsification for dynamic planar graph algorithms","authors":"D. Eppstein, Z. Galil, G. Italiano, T. Spencer","doi":"10.1145/167088.167159","DOIUrl":"https://doi.org/10.1145/167088.167159","url":null,"abstract":"We describe algorithms and data structures for maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We give a fully dynamic planarity testing algorithm that maintains a graph subject to edge insertions and deletions, and allows queries that test whether the graph is currently planar, or whether a potential new edge would violate planarity, in amortized time O(nl 12) per update or query. We maintain the 2and 3-vertex-connected components, and the 3and 4-edge-connected components of a planar graph in O(n.llz ) time per insertion, deletion or query. We give fully dynamic algorithms for maintaining the connected components, the 2-edge-connected components, and the minimum spanning forest of a planar graph in time (9(log n) per insertion and 0(log2 n) per deletion, assuming that insertions keep the graph planar. All our algorithms improve previous bounds: the improvements are based upon a new type of sparsification combined wit h several properties of separators in planar graphs.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129379259","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 the hardness of approximating minimization problems","authors":"C. Lund, M. Yannakakis","doi":"10.1145/167088.167172","DOIUrl":"https://doi.org/10.1145/167088.167172","url":null,"abstract":"We prove results indicating that it is hard to compute efficiently good approximate solutions to the Graph Coloring, Set Covering and other related minimization problems. Specifically, there is an c >0 such that Graph Coloring cannot be approximated with ratio n’ unless P=NP. Set Covering cannot be approximated with ratio clog n for any c < 1/4 unless NP is contained in DTIME[nPOIY log ~ ]. Similar results follow for related problems such as Clique Cover, Fractional Chromatic Number, Dominating Set and others.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114378301","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":"Efficient learning of typical finite automata from random walks","authors":"Y. Freund, M. Kearns, D. Ron, R. Rubinfeld, R. Schapire, Linda Sellie","doi":"10.1145/167088.167191","DOIUrl":"https://doi.org/10.1145/167088.167191","url":null,"abstract":"This paper describes new and efficient algorithms for learning deterministic finite automata. Our approach is primarily distinguished by two features: (1) the adoption of an average-case setting to model the ``typical'' labeling of a finite automaton, while retaining a worst-case model for the underlying graph of the automaton, along with (2) a learning model in which the learner is not provided with the means to experiment with the machine, but rather must learn solely by observing the automaton's output behavior on a random input sequence. The main contribution of this paper is in presenting the first efficient algorithms for learning nontrivial classes of automata in an entirely passive learning model. We adopt an on-line learning model in which the learner is asked to predict the output of the next state, given the next symbol of the random input sequence; the goal of the learner is to make as few prediction mistakes as possible. Assuming the learner has a means of resetting the target machine to a fixed start state, we first present an efficient algorithm that article no. IC972648","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114832080","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":"Efficient probabilistically checkable proofs and applications to approximations","authors":"M. Bellare, S. Goldwasser, C. Lund, Alexander Russell","doi":"10.1145/167088.167174","DOIUrl":"https://doi.org/10.1145/167088.167174","url":null,"abstract":"Efficient Probabilistically Checkable Proofs and Applications to Approximation M. BELLARE* S. GOLDWASSERt C. LUNDi A. RUSSELL$ We construct multi-prover proof systems for NP which use only a constant number of provers to simultaneously achieve low error, low randomness and low answer size. As a consequence, we obtain asymptotic improvements to approximation hardness results for a wide range of optimization problems including minimum set cover, dominating set, maximum clique, chromatic number, and quartic programming; and constant factor improvements on the hardness results for MAXSNP problems. In particular, we show that approximating minimum set cover within any constant is NP-complete; approximating minimum set cover within c log n, for c < 1/8, implies NP C DTIME(nlOglOgn); approximat— ing the maximum of a quartic program within any constant is NP-complete; approximating maximum clique or chromatic number within nl/29 implies NP ~ BPP; and approximating MAX-3 SAT within 113/112 is NPcomplete. * High Performance Computing and Communications, IBM T.J. Watson Research Center, PO Box 704, Yorktown Heights, NY 10598, USA. e-mail: mihirf.Qwatson. ibm. corn. t MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA. e-mail: shaf i@theory. lcs. init. edu. Partially supported by NSF FAW grant No. 9023312-CCR, DARPA g-rant No. NOO014-92-J-1799, and grant No. 89-00312 from the United States Israel Binationsl Science Foundation (BSF), Jerusalem, Israel. $ AT&T Bell Laboratories, Room 2C324, 600 Momtain Avenue, P. O. Box 636, Murray Hill, NJ 07974-0636, USA. email: lund@resesrch. att. corn. $ MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139, USA. e-mail: acrtttheory. lcs. mit . edn. Supported by a NSF Graduate Fellowship and by NSF grant 92-12184, AFOSR 89-0271, and DARPA NOO014-92-J-1799. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,USA","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125289803","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":"Excluded minors, network decomposition, and multicommodity flow","authors":"P. Klein, Serge A. Plotkin, Satish Rao","doi":"10.1145/167088.167261","DOIUrl":"https://doi.org/10.1145/167088.167261","url":null,"abstract":"In this paper we show that, given a graph and parameters 6 and r, we can find either a K,,. minor or an edge-cut of size O(mT/6) whose removal yields components of weak diameter O(T-26); i.e., every pair of nodes in such a component are at distance 0(r26) in the original graph. Using this lemma, we improve the best known bounds for the rein-cut max-flow ratio for mukicommodity flows in graphs with forbidden small minors. In general graphs, it was known that the ratio is O(log k) for the uniform-demand case (the case where there is a unit-demand commodity between every pair of nodes), and that the ratio is 0(log2 k) for arbitrary demands, where k is the number of commodities. In this paper we show that for graphs excluding any fixed graph as a minor (e.g. planar graphs or boundedgenus graphs), the ratio is O(1) for the uniform-demand case and O(log k) for the arbitrary demand case. For such graphs, our method yields rein-ratio cut approximation algorithms with performance bounds that match the above ratios. Computation of such cuts is a basic step for a variety of approximation algorithms for NP-complete problems.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131707862","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-line load balancing with applications to machine scheduling and virtual circuit routing","authors":"J. Aspnes, Y. Azar, A. Fiat, Serge A. Plotkin, Orli Waarts","doi":"10.1145/167088.167248","DOIUrl":"https://doi.org/10.1145/167088.167248","url":null,"abstract":"In this paper we study an idealized problem of on-line allocation of routes to virtual circuits where the goal is to minimize the required bandwidth. For the case where virtual circuits continue to exist forever, we describe an algorithm that achieves an O (log n) competitive ratio, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any on-line algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an on-line scheduling problem, and hence a major part of the paper focuses on development of algorithms for non-preemptive on-line scheduling for related and unrelated machines. Specialization of routing to scheduling leads us to concentrate on scheduling in the case where jobs must be assigned immediately upon arrival; assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrekzted case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, which we show has only a ~(n) competitive ratio. The virtual circuit routing result follows as a generalization of the unrelated machines case.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129509684","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":"Parametric real-time reasoning","authors":"R. Alur, T. Henzinger, Moshe Y. Vardi","doi":"10.1145/167088.167242","DOIUrl":"https://doi.org/10.1145/167088.167242","url":null,"abstract":"Traditional approaches to the algorithmic veri cation of real-time systems are limited to checking program correctness with respect to concrete timing properties (e.g., message delivery within 10 milliseconds\"). We address the more realistic and more ambitious problem of deriving symbolic constraints on the timing properties required of real-time systems (e.g., message delivery within the time it takes to execute two assignment statements\"). To model this problem, we introduce parametric timed automata | nite-state machines whose transitions are constrained with parametric timing requirements. The emptiness question for parametric timed automata is central to the veri cation problem. On the negative side, we show that in general this question is undecidable. On the positive side, we provide algorithms for checking the emptiness of restricted classes of parametric timed automata. The practical relevance of these classes is illustrated with several veri cation examples. There remains a gap between the automata classes for which we know that emptiness is decidable and undecidable, respectively, and this gap is related to various hard and open problems of logic and automata theory.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114618714","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":"Characterizing non-deterministic circuit size","authors":"M. Karchmer, A. Wigderson","doi":"10.1145/167088.167230","DOIUrl":"https://doi.org/10.1145/167088.167230","url":null,"abstract":"Consider the following simple communication problem. Fix a universe U and a family Q of subsets of U. Players I and II receive, respectively, an element a E U and a subset A E Q. Their task is to find a subset B of U such that 1A fl B/ is even and a E B. With every Boolean function f we associate a collection fl~ of subsets of U = f'1 (0), and prove that the (one round) communication complexity of the problem it defines completely determines the szze of the smallest nondeterministic circuit for f. We propose a linear algebraic variant to the general approximation method of Razborov, whtch has exponentially smaller description. We use it to derive four different combinatorial problems (like the one above) that characterize non-uniform NP. These are tight, in the sense that they can be used to prove super-linear circuit size lower bounds. Comb~ned with Ra.zborov]s method, they present a purely combinatorial framework in which to study the P vs. NP vs. co – NP question.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128788203","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":"Cryptographic defense against traffic analysis","authors":"C. Rackoff, Daniel R. Simon","doi":"10.1145/167088.167260","DOIUrl":"https://doi.org/10.1145/167088.167260","url":null,"abstract":"We present a model which allows us formally to define “untraceability” of messages in a network of synchronously communicating processors. We consider several different definitions, based on different assumptions about the strength of the “adversary” attempting to identify the senders and receivers of messages; for example, the adversary may be able to control some of the processors to obtain information, or even disrupt the traffic in the network. We present efficient protocols which are provably secure against each such adversary, using such cryptographic techniques as secure multiparty computation ([ GMWl) and non-interactive zero-knowledge proof ([BFM]). One proof of security also relies on an interesting general lemma about the “mixing” achieved by certain kinds of random processes, or “shuffles”, performed on a set of items. *This work was supported in part by NSERC operating grants and ITRC, an Ontario Centre of Excellence. t Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 1A4; rackoff@cs.toronto. edu : D6partement IRO, Universit6 de Montr6al, C.P. 6128, Succursale “A”, Montr&d, Qu6bec, H3C 3J7; simon@iro.umontreal .ca Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appaar, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA, K.A o 1993 ACM 0-89791 -591 -7/93 /0005 /0672 . ..$1 .50","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126510384","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":"How much can hardware help routing?","authors":"A. Borodin, P. Raghavan, B. Schieber, E. Upfal","doi":"10.1145/167088.167237","DOIUrl":"https://doi.org/10.1145/167088.167237","url":null,"abstract":"We study the extent to which complex hardware can speed up routing. Specifically, we consider the following questions. How much does adaptive routing improve over oblivious routing? How much does randomness help? How does it help if each node can have a large number of neighbors? What benefit is available if a node can send packets to several neighbors within a single time step? Some of these features require complex networking hardware, and it is thus important to investigate whether the performance justifies the investment. By varying these hardware parameters, we obtain a hierarchy of time bounds for worst-case permutation routing.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"211 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115973669","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}