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

{"title":"Checking approximate computations over the reals","authors":"S. Ar, M. Blum, B. Codenotti, P. Gemmell","doi":"10.1145/167088.167288","DOIUrl":"https://doi.org/10.1145/167088.167288","url":null,"abstract":"Checking Approximate Computations over the Reals S. Ar” M. Blumt B. Codenotti$ P. Gemmell~ This paper provides the first systematic investigation of checking approximate numerical computations over subsets of the reals. In most cases, approximate checking is more challenging than exact checking. Problem conditioning, i.e., the measure of sensitivity of the output to slight changes in the input, and the presence of approximate ion parameters foil the direct transformation of many exact checkers to the approximate setting. Furthermore, approximate checking over the reals is complicated by the lack of nice finite field properties such as the existence of a samplable distribution which is invariant under addition or multiplication by a scalar. We overcome the above problems by using such techniques as testing and checking over similar but distinct distributions, using functions’ random and downward self-reducibility properties, and taking advantage of the small variance of the sum of independent identically distributed random variables. We provide approximate checkers for a variety of computations, including matrix multiplication, linear system solution, matrix inversion, and computation of the determinant. We also present an approximate version of Beigel’s trick and extend the approximate linear self tester/corrector of [8] and the trigonometric selftester/corrector of [5] to more general computations. *Department of Computer Science, Princeton University, Princeton, NJ 08544-2087. Supported by NSF PYI grant CCR9057486 and a grant from MITL. t Computer Science Division, UC Berkeley, Berkeley, CA 94720, and International Computer Science Institute, Berkeley CA 94704. Supported by NSF grant CCR88-13632. t International Computer Science Institute, Berkeley, CA 94704, and IEI-CNR, Piss (Italy). Partially supported by the “ Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo”. Subproject 2. e-mail: codenotti@iei.pi .cnr.it ~Computer Science Division, UC Berkeley, Berkeley, CA 94720. Supported by GTE, Schlumberger Fellowships, and by NSF grant CCR88-13632.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"39 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":"114968879","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 linear time algorithm for finding tree-decompositions of small treewidth","authors":"H. Bodlaender","doi":"10.1145/167088.167161","DOIUrl":"https://doi.org/10.1145/167088.167161","url":null,"abstract":"In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"136 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":"122170489","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":"Reinventing the wheel: an optimal data structure for connectivity queries","authors":"R. Cohen, G. Battista, A. Kanevsky, R. Tamassia","doi":"10.1145/167088.167152","DOIUrl":"https://doi.org/10.1145/167088.167152","url":null,"abstract":"We show that, for any fixed k, there exists an optimal O(n)-space compact representation of a k-connected graph G with n vertices, such that one can determine in O(1) time whether two vertices areconnectedbyk+l vertex-dkjoint paths, or are separated by k vertices/edges. Previously, the existence of such compact representations was known only for k <3. 1 Summary of Results A fundamental issue for the fault-tolerance and reliabilityofnetworksis determining the existence of multiple disjoint paths connecting two nodes. In this paper we investigate the problem of constructing a compact representation of a graph so that one can test quickly for the existence of such paths. *Research supported in part by the National ScienceFoundation under grant CCR9007851, by the U.S. Army Research Office under grant DAAL03-91-G-o035, by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract NOO014-91-J-4052, ARPA order 8225, by the NATO Scientific Affairs Division under collaborative research grant 911016, by the Pro get t o Finalimato Sisterni Informatici e Calcolo ParaUelo of the Italian National Research Council, and by the Esprit II BRA of the European Community (project ALCOM). t Department of Computer Science, University of Newcastle, Callaghan, New South Wales 2308, Australia. The work of this author was carried out in part while visiting the United States Coast Guard Academy and Brown University. t Dip=tirnento & Inforrnatica e %ternist.ica, Universit& & Roma ‘[La Sapienza”, Via Salaria 113, 00198 Rome, Italy, 5Department of Computer Science, Texas A&M University, College Station, TX 77843-3112. f Depmtment of Computer Science, Brown University, providence, RI 02912–1910. 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 ‘93-5193 /CA, USA 9 1993 ACM 0-89791 -591 -7/93 /0005 /0794 . ..$1.!50 Given a graph G, we say that vertices v’ and vII of G are k-connected if there are k vertex-diajoint paths between vi and v“. Graph G is said to be kconnected if every pair of vertices is k-connected. Let G be a k-connected graph. A k-cut of G ia a k-tuple U={tl,... t} , k , where each t~ is a vertex or an edge, such that removing U disconnects G. By Menger’a theorem [5], G is (k + I )-connected if and only if it has no k-cut. We say that a k-cut U separates subsets V’ and V“ of vertices if U n V’ = U n V“ = 0, and there ia no connected component of G — U containing vertices of both V’ and V“. A (k + I)-connectivity query for vertices v’ and v“ of a k-connected graph G, denoted (k + I)-Paths(v’, v“), returns -true if v’ and v“ are (k + I)-connected, and otherwise retu","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"76 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":"123159906","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 deterministic algorithm for the three-dimensional diameter problem","authors":"J. Matoušek, O. Cheong","doi":"10.1145/167088.167217","DOIUrl":"https://doi.org/10.1145/167088.167217","url":null,"abstract":"Abstract We give a deterministic algorithm for computing the diameter of an n-point set in three dimensions with O(n logcn) running time, where c is a constant.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"6 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":"114388368","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":"Depth reduction for noncommutative arithmetic circuits","authors":"E. Allender, Jia Jiao","doi":"10.1145/167088.167226","DOIUrl":"https://doi.org/10.1145/167088.167226","url":null,"abstract":"We show that for every family of arithmetic circuits of polynomial size and degree over the algebra (Z*, max, concat ), there is an equivalent family of arithmetic circuits of depth log2 n. (The depth can be reduced to log n if unbounded fan-in is allowed.) This is the first depth-reduction result for arithmetic circuits Olrer a nonco~utative semiring, and it complements the lower bounds of [Ni91, K090] showing that depth reduction cannot be done in the general noncommutative setting. The (max,concat) semiring is of interest, because it characterizes certain classes of optimization problems [AJ92, Vi91]. In particular, our results show that OptSACi is contained in AC1. We also prove other results relating Boolean and arithmetic circuit complexity. We show that ACl has no more power than arithmetic circuits of polynomial size and degree n“(log log’) (improving the trivial bound of nOIIOg‘)). Connections are drawn between TCl and arithmetic circuits of polynomial size and degree.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"23 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":"133042927","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":"Lower bounds for randomized mutual exclusion","authors":"E. Kushilevitz, Y. Mansour, M. Rabin, David Zuckerman","doi":"10.1145/167088.167139","DOIUrl":"https://doi.org/10.1145/167088.167139","url":null,"abstract":"We establish, for the rst time, lower bounds for randomized mutual exclusion algorithms (with a read-modify-write operation). Our main result is that a constant-size shared variable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of ›(log logn) bits on the size of the shared variable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that slightly weakening the fairness condition results in an exponential reduction in the size of the required shared variable. Our lower bounds rely on an analysis of Markov chains that may be of interest on its own and may have applications elsewhere.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"162 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":"133117804","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":"Matrix searching with the shortest path metric","authors":"J. Hershberger, S. Suri","doi":"10.1145/167088.167220","DOIUrl":"https://doi.org/10.1145/167088.167220","url":null,"abstract":"We present an O(n) time algorithm for computing row-wise maxima or minima of an implicit, totally monotone nn matrix whose entries represent shortest-path distances between pairs of vertices in a simple polygon. We apply this result to derive improved algorithms for several well- known problems in computational geometry. Most prominently, we obtain linear-time algorithms for computing the geodesic diameter, all farthest neighbors, and external farthest neighbors of a simple polygon, improving the previous best result by a factor of O(logn) in each case.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"28 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":"123659012","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 noise-tolerant learning from statistical queries","authors":"M. Kearns","doi":"10.1145/167088.167200","DOIUrl":"https://doi.org/10.1145/167088.167200","url":null,"abstract":"In this paper, we study the problem of learning in the presence of classification noise in the probabilistic learning model of Valiant and its variants. In order to identify the class of “robust” learning algorithms in the most general way, we formalize a new but related model of learning from statistical queries. Intuitively, in this model, a learning algorithm is forbidden to examine individual examples of the unknown target function, but is given access to an oracle providing estimates of probabilities over the sample space of random examples. One of our main results shows that any class of functions learnable from statistical queries is in fact learnable with classification noise in Valiant’s model, with a noise rate approaching the informationtheoretic barrier of 1/2. We then demonstrate the generality of the statistical query model, showing that practically every class learnable in Valiant’s model and its variants can also be learned in the new model (and thus can be learned in the presence of noise). A notable exception to this statement is the class of parity functions, which we prove is not learnable from statistical queries, and for which no noise-tolerant algorithm is known.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"29 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":"125425398","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":"Probabilistically checkable debate systems and approximation algorithms for PSPACE-hard functions","authors":"A. Condon, J. Feigenbaum, C. Lund, P. Shor","doi":"10.1145/167088.167190","DOIUrl":"https://doi.org/10.1145/167088.167190","url":null,"abstract":"We initiate an investigation of probabilistically check-able debate systems (PCDS'S), a natural generalization of the probabilistically checkable proof systems studied in [1, 2, 3, 8]. A PCDS for a language L consists of a probabilistic polynomial-time verifier V and a debate between player 1, who claims that the input z is in L, and player O, who claims that the input x is not in L. We show that there is a PCDS for L in which V flips O(log n) random coins and reads O(1) bits of the debate if and only if L is in PSPACE. This characterization of PSPACE is used to show that certain PSPACE-hard functions are as hard to approximate as they are to compute exactly. * The full version of this paper has been submitted for journal publication and is available as DIMACS TR 93-1o. 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. 1 Introduction Suppose that two candidates, B and C, agree to a debate format. Voter V is too busy to catch more than a very small number of bits of the debate. How does V decide which of B or C won the debate? In this paper , we show that if B and C choose the right debate format, V's problem is solved. By listening to a few, randomly chosen, sounds bites of the debate, V can with near certainty figure out who won. Similarly, suppose that B or C is giving a speech to a set of voters VI,. .. . Vn, represented by finite au-tomata. He would like to give the speech that results in acceptance (votes) by the greatest number of Vi 's, We show that not only can he not compute this maximum exactly, but he cannot come within an arbitrary constant factor, unless he has access to an oracle (political consultant) with the full power of P!3PACE. Our work builds on the recent progress that has been made in the theory of probabilistically checkable proof systems (PCPS 's). Results about the language.-recognition power of PCPS'S have …","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"47 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":"115310057","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":"Generalized FLP impossibility result for t-resilient asynchronous computations","authors":"E. Borowsky, E. Gafni","doi":"10.1145/167088.167119","DOIUrl":"https://doi.org/10.1145/167088.167119","url":null,"abstract":"Demarcation of the border between solvable and unsolvable distributed tdis under various models is the holy grail of the theory of distributed computing. Oneof the most celebrated of theseresults is [6] (FLP) which established the impossibility of asynchronous consensus that can tolerate a single undetected fail-stop processor. This paper generalizes FLP to multiple faults. It establishes that k-set consensus proposed by Chaudhuri is impossible, if the protocol is to tolerate k failures, while there exists a protocol that tolerates k – 1 failures. Our proof technique is completely different than the one employed in [6]. We introduce a new model of computation, the im112ecliate-atoY12 ic-.s?2u~)shot. We fully characterize the graph of waitfree views within the model. Applying a variant of Sperner Lemma to this graph establishes the impossibility of k + 1 processors achieving waitfree k-set consensus. Finally, we introduce a new notion of nonblocking-busy-wait agreement protocol, With this ● Work supported by NSF Presiciential Young Iavest,igator Award under grant DCR84-51396 . Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direot commercial advantage, the ACM copyright notica and the title of the publication and its data appear, and notica is givan that copying is by permission of the Association for Computing Machinery. To copy otherwisa, or to republish, requiras a fea and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ 1993 ACM 0.89791.591-7/93/0005/0091 .,C$l .5(3 protocol we construct a read/write waitfree simulation techniclue by which k + 1 processors can produce a k-faulty execution of n processors protocol, {Tsing the simulation we establish the impossibility of n processors protocol that achieves k-set consensus and tolerates k failures, by reducing it to the waitfree case.","PeriodicalId":280602,"journal":{"name":"Proceedings of the twenty-fifth annual ACM symposium on Theory of Computing","volume":"29 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":"127227386","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}