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Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science最新文献

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On choosing a dense subgraph 关于选择稠密子图
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366818
G. Kortsarz, D. Peleg
{"title":"On choosing a dense subgraph","authors":"G. Kortsarz, D. Peleg","doi":"10.1109/SFCS.1993.366818","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366818","url":null,"abstract":"This paper concerns the problem of computing the densest k-vertex subgraph of a given graph, namely, the subgraph with the most edges, or with the highest edges-to-vertices ratio. A sequence of approximation algorithms is developed for the problem, with each step yielding a better ratio at the cost of a more complicated solution. The approximation ratio of our final algorithm is O/spl tilde/(n/sup 0.3885/). We also present a method for converting an approximation algorithm for an unweighted graph problem (from a specific class of maximization problems) into one for the corresponding weighted problem, and apply it to the densest subgraph problem.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127050602","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: 139
NP trees and Carnap's modal logic NP树和卡尔纳普的模态逻辑
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1145/201019.201031
G. Gottlob
{"title":"NP trees and Carnap's modal logic","authors":"G. Gottlob","doi":"10.1145/201019.201031","DOIUrl":"https://doi.org/10.1145/201019.201031","url":null,"abstract":"We consider problems and complexity classes definable by interdependent queries to an oracle in NP. How the queries depend on each other is specified by a directed graph G. We first study the class of problems where G is a general dag and show that this class coincides with /spl Delta//sub 2//sup P/. We then consider the class where G is a tree. Our main result states that this class is identical to P/sup NP/ [O(log n)], the class of problems solvable in polynomial time with a logarithmic number of queries to an oracle in NP. Using this result we show that the following problems are all P/sup NP/[O(logn)] complete: validity-checking of formulas in Carnap's modal logic, checking whether a formula is almost surely valid over finite structures in modal logics K, T, and S4, and checking whether a formula belongs to the stable set of beliefs generated by a propositional theory.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130663604","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: 65
An O(nlog/sup 3/ n) algorithm for the real root problem 实根问题的O(nlog/sup 3/ n)算法
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366824
J. Reif
{"title":"An O(nlog/sup 3/ n) algorithm for the real root problem","authors":"J. Reif","doi":"10.1109/SFCS.1993.366824","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366824","url":null,"abstract":"Given a univariate complex polynomial f(x) of degree n with rational coefficients expressed as a ratio of two integers <2/sup m/, the root problem is to find all the roots of f(x) up to specified precision 2/sup -/spl mu//. In this paper we assume the arithmetic model for computation. We give an algorithm for the real root problem: where all the roots of the polynomial are real. Our real root algorithm has time cost of O(nlog/sup 2/ n(log n+log b)), where b=m+/spl mu/, thus has time bound O(nlog/sup 3/ n) even in the case of high precision m+/spl mu//spl les/n/sup O(1/). This is within a small polylog factor of optimality, thus (perhaps surprisingly) upper bounding the arithmetic complexity of our real root problem to nearly the same as basic arithmetic operations on polynomials. We require only /spl pi/=O(n(/spl mu/+m+n)) bits of precision to carry out our computations. The Boolean complexity of our algorithm is a multiplicative factor of M(/spl pi/)=O(/spl pi/(log /spl pi/)loglog /spl pi/) more.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133646087","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: 11
Top-down lower bounds for depth 3 circuits 深度3电路自上而下的下界
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366875
J. Håstad, S. Jukna, P. Pudlák
{"title":"Top-down lower bounds for depth 3 circuits","authors":"J. Håstad, S. Jukna, P. Pudlák","doi":"10.1109/SFCS.1993.366875","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366875","url":null,"abstract":"We present a top-down lower bound method for depth 3 AND-OR-NOT circuits which is simpler than the previous methods and in some cases gives better lower bounds. In particular we prove that depth 3 AND-OR-NOT circuits that compute PARITY resp. MAJORITY require size at least 2/sup 0.618/ .../spl radic/n/ resp. 2/sup 0.849/.../spl radic/n/. This is the first simple proof of a strong lower bound by a top-down argument for non-monotone circuits.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132267492","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: 21
The hardness of approximate optima in lattices, codes, and systems of linear equations 格、码和线性方程组中近似最优解的硬度
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366815
Sanjeev Arora, L. Babai, J. Stern, E. Sweedyk
{"title":"The hardness of approximate optima in lattices, codes, and systems of linear equations","authors":"Sanjeev Arora, L. Babai, J. Stern, E. Sweedyk","doi":"10.1109/SFCS.1993.366815","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366815","url":null,"abstract":"We prove the following about the Nearest Lattice Vector Problem (in any l/sub p/ norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NP-hard. 2. If for some /spl epsiv/>0 there exists a polynomial time algorithm that approximates the optimum within a factor of 2/sup log(0.5-/spl epsiv/)/ /sup n/ then NP is in quasi-polynomial deterministic time: NP/spl sube/DTIME(n/sup poly(log/ /sup n)/). Moreover, we show that result 2 also holds for the Shortest Lattice Vector Problem in the l/sub /spl infin// norm. Improving the factor 2/sup log(0.5-/spl epsiv/)/ /sup n/ to /spl radic/(dim) for either of the lattice problems would imply the hardness of the Shortest Vector Problem in l/sub 2/ norm; an old open problem. Our proofs use reductions from few-prover, one-round interactive proof systems, either directly, or through a set-cover problem.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129363137","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: 491
Parallel computable higher type functionals 并行可计算的高级函数
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366880
P. Clote, A. Ignjatović, B. Kapron
{"title":"Parallel computable higher type functionals","authors":"P. Clote, A. Ignjatović, B. Kapron","doi":"10.1109/SFCS.1993.366880","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366880","url":null,"abstract":"The primary aim of this paper is to introduce higher type analogues of some familiar parallel complexity classes, and to show that these higher type classes can be characterised in significantly different ways. Recursion-theoretic, proof-theoretic and machine-theoretic characterisations are given for various classes, providing evidence of their naturalness.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123599309","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: 5
Signal propagation, with application to a lower bound on the depth of noisy formulas 信号的传播，用应用于噪声深度下界的公式
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366827
W. Evans, L. Schulman
{"title":"Signal propagation, with application to a lower bound on the depth of noisy formulas","authors":"W. Evans, L. Schulman","doi":"10.1109/SFCS.1993.366827","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366827","url":null,"abstract":"We study the decay of an information signal propagating through a series of noisy channels. We obtain exact bounds on such decay, and as a result provide a new lower bound on the depth of formulas with noisy components. This improves upon previous work of N. Pippenger (1988) and significantly decreases the gap between his lower bound and the classical upper bound of von Neumann. We also discuss connections between our work and the study of mixing rates of Markov chains.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"168 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124684289","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: 29
A simple local-control approximation algorithm for multicommodity flow 多商品流的简单局部控制逼近算法
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366841
B. Awerbuch, F. Leighton
{"title":"A simple local-control approximation algorithm for multicommodity flow","authors":"B. Awerbuch, F. Leighton","doi":"10.1109/SFCS.1993.366841","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366841","url":null,"abstract":"In this paper, we describe a very simple (1+/spl epsi/)-approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and /spl epsiv//sup -1/ (the closeness of the approximation to optimal). The algorithm is remarkable in that it is much simpler than all known polynomial time flow algorithms (including algorithms for the special case of one-commodity flow). In particular, the algorithm does not rely on augmenting paths, shortest paths, min-cost paths, or similar techniques to push flow through a network. In fact, no explicit attempt is ever made to push flow towards a sink during the algorithm. Because the algorithm is so simple, it can be applied to a variety of problems for which centralized decision making and flow planning is not possible. For example, the algorithm can be easily implemented with local control in a distributed network and it can be made tolerant to link failures. In addition, the algorithm appears to perform well in practice. Initial experiments using the DIMACS generator of test problems indicate that the algorithm performs as well as or better than previously known algorithms, at least for certain test problems.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129269024","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: 143
A weak version of the Blum, Shub and Smale model 一个弱版本的Blum, Shub和small模型
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366838
P. Koiran
{"title":"A weak version of the Blum, Shub and Smale model","authors":"P. Koiran","doi":"10.1109/SFCS.1993.366838","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366838","url":null,"abstract":"We propose a weak version of the Blum-Shub-Smale model (1989) of computation over the real numbers. In this weak model only a \"moderate\" usage of multiplications and divisions is allowed. The class of languages recognizable in polynomial time as shown to be the complexity class P/poly. This implies under a standard complexity-theoretic assumption that P/spl ne/NP in the weak model, and that problems such as the real traveling salesman problem cannot be solved in polynomial time. As an application, we generalize recent results of H.T. Siegelmann and E.D. Sontag (1993) on recurrent neural networks, and of W. Maass (1993) on feedforward nets.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127872130","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: 76
Las Vegas algorithms for matrix groups 矩阵群的拉斯维加斯算法
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science Pub Date : 1993-11-03 DOI: 10.1109/SFCS.1993.366844
R. Beals, L. Babai
{"title":"Las Vegas algorithms for matrix groups","authors":"R. Beals, L. Babai","doi":"10.1109/SFCS.1993.366844","DOIUrl":"https://doi.org/10.1109/SFCS.1993.366844","url":null,"abstract":"We consider algorithms in finite groups, given by a list of generators. We give polynomial time Las Vegas algorithms (randomized, with guaranteed correct output) for basic problems for finite matrix groups over the rationals (and over algebraic number fields): testing membership, determining the order, finding a presentation (generators and relations), and finding basic building blocks: center, composition factors, and Sylow subgroups. These results extend previous work on permutation groups into the potentially more significant domain of matrix groups. Such an extension has until recently been considered intractable. In case of matrix groups G of characteristic p, there are two basic types of obstacles to polynomial-time computation: number theoretic (factoring, discrete log) and large Lie-type simple groups of the same characteristic p involved in the group. The number theoretic obstacles are inherent and appear already in handling abelian groups. They can be handled by moderately efficient (subexponential) algorithms. We are able to locate all the nonabelian obstacles in a normal subgroup N and solve all problems listed above for G/N.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128005694","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: 48
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