{"title":"ERROR-CORRECTING DATA STRUCTURES ∗","authors":"Victor Chen, E. Grigorescu, Ronald de Wolf","doi":"10.1137/110834949","DOIUrl":"https://doi.org/10.1137/110834949","url":null,"abstract":"We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been corrupted by a constant fraction of errors. We measure the efficiency of a data structure in terms of its length (the number of bits in its representation) and query-answering time, measured by the number of bit-probes to the (possibly corrupted) representation. The main issue is the trade-off between these two. This new model is the common generalization of (static) data structures and locally decodable error-correcting codes (LDCs). We prove a number of upper and lower bounds on various natural error-correcting data structure problems. In particular, we show that the optimal length of $t$-probe error-correcting data structures for the Membership problem (where we want to store subsets of size $s$ from a universe of size $n$ such that membership queries can be answered effic...","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"32 1","pages":"84-111"},"PeriodicalIF":1.6,"publicationDate":"2013-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89790534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits","authors":"DvirZeev, ShpilkaAmir, YehudayoffAmir","doi":"10.5555/1957995.1957999","DOIUrl":"https://doi.org/10.5555/1957995.1957999","url":null,"abstract":"In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exi...","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"46 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2009-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81211582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jianer Chen, Joachim Kneis, Songjian Lu, D. Mölle, Stefan Richter, P. Rossmanith, S. Sze, Fenghui Zhang
{"title":"Randomized Divide-and-Conquer: Improved Path, Matching, and Packing Algorithms","authors":"Jianer Chen, Joachim Kneis, Songjian Lu, D. Mölle, Stefan Richter, P. Rossmanith, S. Sze, Fenghui Zhang","doi":"10.1137/080716475","DOIUrl":"https://doi.org/10.1137/080716475","url":null,"abstract":"We propose a randomized divide-and-conquer technique that leads to improved randomized and deterministic algorithms for NP-hard path, matching, and packing problems. For the parameterized max-path problem, our randomized algorithm runs in time $O(4^{k}k^{2.7}m)$ and polynomial space (where m is the number of edges in the input graph), improving the previous best randomized algorithm for the problem that runs in time $O(5.44^{k}km)$ and exponential space. Our randomized algorithms for the parameterized max r-d matching and max r-set packing problems run in time $4^{(r-1)k}n^{O(1)}$ and polynomial space, improving the previous best algorithms for the problems that run in time $10.88^{rk}n^{O(1)}$ and exponential space. Moreover, our randomized algorithms can be derandomized to result in significantly improved deterministic algorithms for the problems, and they can be extended to solve other matching and packing problems.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"73 1","pages":"2526-2547"},"PeriodicalIF":1.6,"publicationDate":"2009-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84340477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Size-Space Tradeoffs for Resolution","authors":"Eli Ben-Sasson","doi":"10.1137/080723880","DOIUrl":"https://doi.org/10.1137/080723880","url":null,"abstract":"We investigate tradeoffs of various basic complexity measures such as size, space, and width. We show examples of formulas that have optimal proofs with respect to any one of these parameters, but optimizing one parameter must cost an increase in the other. These results have implications to the efficiency (or rather, inefficiency) of some commonly used SAT solving heuristics. Our proof relies on a novel connection of the variable space of a proof to the black-white pebbling measure of an underlying graph.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"53 1","pages":"2511-2525"},"PeriodicalIF":1.6,"publicationDate":"2009-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78599969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ronald Fagin, Anupam Gupta, Ravi Kumar, R. O'Donnell
{"title":"Special Issue Dedicated to the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC 2005)","authors":"Ronald Fagin, Anupam Gupta, Ravi Kumar, R. O'Donnell","doi":"10.1137/SMJCAT000038000002000vii000001","DOIUrl":"https://doi.org/10.1137/SMJCAT000038000002000vii000001","url":null,"abstract":"This volume comprises the polished and fully refereed versions of a selection of papers presented at the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC 2005), held in Baltimore, Maryland, May 22-24, 2005. Unrefereed preliminary versions of the papers presented at the symposium appeared in the proceedings of the meeting, published by ACM. The symposium was sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). \u0000 \u0000The STOC 2005 Program Committee consisted of Gerth Stolting Brodal, Harry Buhrman, Jin-Yi Cai, Cynthia Dwork, Ronald Fagin (chair), Martin Farach-Colton, Anupam Gupta, Sariel Har-Peled, Russell Impagliazzo, Kamal Jain, Adam Tauman Kalai, David Karger, Claire Kenyon, Subhash Khot, Ravi Kumar, Moni Naor, Ryan O'Donnell, Toniann Pitassi, Tim Roughgarden, Alistair Sinclair, and Amnon Ta-Shma. \u0000 \u0000Out of 290 “Extended Abstracts” submitted to the STOC 2005 Program Committee, 84 were selected for presentation at the symposium. The present volume includes 9 of these papers that were invited to this volume. All papers were refereed in accordance with the SIAM Journal on Computing's stringent standards, and these papers were substantially updated in the process. We take this opportunity to thank all the referees whose anonymous work has significantly contributed to the value of this volume. \u0000 \u0000Ronald Fagin, the Program Chair of the 2005 STOC Conference, invited three other members of the Program Committee (Anupam Gupta, Ravi Kumar, and Ryan O'Donnell) to assist in editing this special issue of the of the SIAM Journal on Computing, and all agreed. We feel that it was an honor to edit this issue.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"205 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2008-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73370499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Chosen-Ciphertext Security from Identity-Based Encryption","authors":"D. Boneh, Ran Canetti, S. Halevi, Jonathan Katz","doi":"10.1137/S009753970544713X","DOIUrl":"https://doi.org/10.1137/S009753970544713X","url":null,"abstract":"We propose simple and efficient CCA-secure public-key encryption schemes (i.e., schemes secure against adaptive chosen-ciphertext attacks) based on any identity-based encryption (IBE) scheme. Our constructions have ramifications of both theoretical and practical interest. First, our schemes give a new paradigm for achieving CCA-security; this paradigm avoids “proofs of well-formedness” that have been shown to underlie previous constructions. Second, instantiating our construction using known IBE constructions we obtain CCA-secure encryption schemes whose performance is competitive with the most efficient CCA-secure schemes to date. Our techniques extend naturally to give an efficient method for securing IBE schemes (even hierarchical ones) against adaptive chosen-ciphertext attacks. Coupled with previous work, this gives the first efficient constructions of CCA-secure IBE schemes.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"260 1","pages":"1301-1328"},"PeriodicalIF":1.6,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77140729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Probabilistic Approach to the Dichotomy Problem","authors":"Tomasz Łuczak, J. N. caron, etr caron, il","doi":"10.1137/S0097539703435492","DOIUrl":"https://doi.org/10.1137/S0097539703435492","url":null,"abstract":"Let ${mathcal R}(n,k)$ denote the random $k$-ary relation defined on the set $[n]={1,2,dots,n}$. We show that the probability that $([n], {mathcal R}(n,k))$ is projective tends to one, as either $n$ or $k$ tends to infinity. This result implies that for most relational systems $(B,{{underline{R}}})$ the ${{textrm{CSP}}}(B,{{underline{R}}})$ problem is NP-complete (and thus that the dichotomy conjecture holds with probability 1), and confirms a conjecture of Rosenberg [I. G. Rosenberg, Rocky Mountain J. Math., 3 (1973), pp. 631-639].","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"23 1","pages":"835-843"},"PeriodicalIF":1.6,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73640175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A 2-Approximation Algorithm for the Directed Multiway Cut Problem","authors":"Siam Staff","doi":"10.1137/S009753979732147X","DOIUrl":"https://doi.org/10.1137/S009753979732147X","url":null,"abstract":"A directed multiway cut separates a set of terminals T={s1, . . . , sk} in a directed capacitated graph G=(V,E). Finding a minimum directed multiway cut is an NP-hard problem. We give a polynomial-time algorithm that achieves an approximation factor of 2 for this problem. This improves the result of Garg, Vazirani, and Yannakakis [Proceedings of the 21st International Colloquium on Automata, Languages, and Programming, Jerusalem, Israel, 1994, pp. 487--498], who gave an algorithm that achieves an approximation factor of 2 log k. Our approximation algorithm uses a novel technique for relaxing a multiway flow function in order to find a directed multiway cut. It also implies that the integrality gap of the linear program for the directed multiway cut problem is at most 2.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"91 1","pages":"477-482"},"PeriodicalIF":1.6,"publicationDate":"2002-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80488660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Total Coloring With $Delta + mboxlowercasepoly(log Delta)$ Colors","authors":"H. Hind, Michael Molloy, B. Reed","doi":"10.1137/S0097539795294578","DOIUrl":"https://doi.org/10.1137/S0097539795294578","url":null,"abstract":"We provide a polynomial time algorithm which finds a total coloring of any graph with maximum degree $D$, $D$ sufficiently large, using at most $D+8log^8D$ colors. This improves the best previous upper bound on the total chromatic number of $D+18D^{1/3}log(3D)$.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"30 1","pages":"816-821"},"PeriodicalIF":1.6,"publicationDate":"1999-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84836350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Computational Power of Frictional Mechanical Systems","authors":"John Z. Sun","doi":"10.1201/9781439863886-24","DOIUrl":"https://doi.org/10.1201/9781439863886-24","url":null,"abstract":"In this paper we deene a class of mechanical systems consisting of rigid objects (deened by linear or quadratic surface patches) connected by frictional contact linkages between surfaces. (This class of mechanisms is similar to the Analytical Engine developed by Babbage in 1800s except that we assume frictional surfaces instead of toothed gears.) We prove that a universal Turing Machine (TM) can be simulated by a (universal) frictional mechanical system in this class. Our universal frictional mechanical system has the property that it can reach a distinguished nal conngura-tion through a sequence of legal movements if and only if the universal TM accepts the input string encoded by its initial connguration. There are two implications from this result. First, the mover's problem is undecid-able when there are frictional linkages. Second, a mechanical computer can be constructed that has the computational power of any conventional electronic computer and yet has only a constant number of mechanical parts. Previous constructions for mechanical computing devices (such as Babbage's Analytical Engine) either provided no general construction for nite state control or the control was provided by electronic devices (as was common in electro-mechanical computers such as Mark I subsequent to Turing's result). Our result seems to be the rst to provide a general proof of the simulation of a universal TM via a purely mechanical mechanism. In addition, we discuss the universal frictional mechanical system in the context of an error model that allows error up to in each mechanical operation. First, we show that for a universal TM M, a frictional mechanical system of this-error model can be constructed such that, given any space bound S, the system can simulate the computation of M on any input string ! if M decides ! in space bound S, provided that < 2 ?cS for some constant c. Second, we show that, for any universal TM M and space bound S, if we let = O(S ?1), there exists a frictional mechanical system in the-error model that can simulate M on any input which M decides in space bound S.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"1998-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88962007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}