26th Annual Symposium on Foundations of Computer Science (sfcs 1985)最新文献

The least weight subsequence problem 最小权值子序列问题

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1987-08-01 DOI: 10.1137/0216043

D. Hirschberg, L. Larmore

引用次数: 85

The bit extraction problem or t-resilient functions 钻头提取问题或t弹性函数

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.55

B. Chor, Oded Goldreich, J. Håstad, J. Friedman, S. Rudich, R. Smolensky

引用次数: 384

Deterministic simulation of probabilistic constant depth circuits 概率定深电路的确定性仿真

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.19

M. Ajtai, A. Wigderson

{"title":"Deterministic simulation of probabilistic constant depth circuits","authors":"M. Ajtai, A. Wigderson","doi":"10.1109/SFCS.1985.19","DOIUrl":"https://doi.org/10.1109/SFCS.1985.19","url":null,"abstract":"We explicitly construct, for every integer n and ε ≫ 0, a family of functions (psuedo-random bit generators) fn,ε:{0,1}nε → {0,1}n with the following property: for a random seed, the pseudorandom output \"looks random\" to any polynomial size, constant depth, unbounded fan-in circuit. Moreover, the functions fn,ε themselves can be computed by uniform polynomial size, constant depth circuits. Some (interrelated) consequences of this result are given below. 1) Deterministic simulation of probabilistic algorithms. The constant depth analogues of the probabilistic complexity classes RP and BPP are contained in the deterministic complexity classes DSPACE(nε) and DTIME(2nε) for any ε ≫ 0. 2) Making probabilistic constructions deterministic. Some probablistic constructions of structures that elude explicit constructions can be simulated in the above complexity classes. 3) Approximate counting. The number of satisfying assignments to a (CNF or DNF) formula, if not too small, can be arbitrarily approximated in DSPACE(nε) and DTIME(2nε), for any ε ≫ 0. We also present two results for the special case of depth 2 circuits. They deal, respectively, with finding a satisfying assignment and approximately counting the number of assignments. For example, for 3-CNF formulas with a fixed fraction of satisfying assignmemts, both tasks can be performed in polynomial time!","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121629713","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: 104

Computing with polynomials given by straight-line programs II sparse factorization 由直线程序给出的多项式的计算II稀疏分解

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.17

E. Kaltofen

引用次数: 25

Algebraic cell decomposition in NC NC中的代数单元分解

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.4

D. Kozen, C. Yap

引用次数: 69

A scaling algorithm for weighted matching on general graphs 一般图的加权匹配缩放算法

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.3

H. Gabow

引用次数: 111

Partial polymorphic type inference is undecidable 部分多态型推断是不可确定的

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.44

H. Boehm

引用次数: 52

Using dual approximation algorithms for scheduling problems: Theoretical and practical results 用对偶逼近算法求解调度问题:理论与实践结果

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1145/7531.7535

D. Hochbaum, D. Shmoys

{"title":"Using dual approximation algorithms for scheduling problems: Theoretical and practical results","authors":"D. Hochbaum, D. Shmoys","doi":"10.1145/7531.7535","DOIUrl":"https://doi.org/10.1145/7531.7535","url":null,"abstract":"The problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well-studied problem in the theory of approximation algorithms for NP-hard optimization problems. In this paper we present the strongest possible type of result for this problem, a polynomial approximation scheme. More precisely, for each ε, we give an algorithm that runs in time O((n/ε)1/ε2) and has relative error at most ε. For algorithms that are polynomial in n and m, the strongest previously-known result was that the MULTIFIT algorithm delivers a solution with no worse than 20% relative error. In addition, we present a refinement of our scheme in the case where the performance guarantee is equal to that of MUL-TIFIT, that yields an algorithm that is both more efficient and easier to analyze than MULTIFIT. In this case, in order to guarantee a maximum relative error of 1/5+2-k, the algorithm runs in O(n(k+logn)) time. The scheme is based on a new approach to constructing approximation algorithms, which we call dual approximation algorithms, where the aim is find superoptimal, but infeasible solutions, and the performance is measured by the degree of infeasibility allowed. This notion should find wide applicability in its own right, and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132834552","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: 720

The complexity of parallel computation on matroids 拟阵上并行计算的复杂性

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.57

R. Karp, E. Upfal, A. Wigderson

{"title":"The complexity of parallel computation on matroids","authors":"R. Karp, E. Upfal, A. Wigderson","doi":"10.1109/SFCS.1985.57","DOIUrl":"https://doi.org/10.1109/SFCS.1985.57","url":null,"abstract":"In [KUW1] we have proposed the setting of independence systems to study the relation between the computational complexity of search and decision problems. The universal problem that captures this relation, which we termed the S-search problem, is: \"Given an oracle for the input system, find a maximal independent subset in it\". Many interesting and important search problems can be described by a special class of independence systems, called matroids. This paper is devoted to die complexity of the S- search problem for matroids. Our main result is a lower bound on any probabilistic algorithm for the S-search problem that acquires information about the input system by interrogating an independence oracle. We prove that the expected time of any such probabilistic algorithm that uses a sub-exponential number of processors is Ω(n1/3-ε). This is one of the first nontrivial, super-logarithmic lower bounds on a randomized parallel computation. It implies that in our model of computation Random-NC is strictly contained in P. Another consequence of the lower bound is that the O(√n) time probabilistic upper bound for arbitrary independence systems, presented in [KUW1], is close to optimal and cannot be significantly improved, even for matroids. However, fills O(√n) upper bound can be improved in a different sense for matroids -it can be made deterministic, still with polynomially many processors. Finally, we show that the lower bound can be beaten for the special case of graphic matroids. Here, the S-search problem is simply to find a spanning forest of a graph, when the algorithm cannot see the graph, but can only ask whether subsets of edges are forests or not. We give an O(logn) time deterministic parallel algoritlun that uses nO(logn) processors. From the upper bounds on parallel time above we deduce similar bounds (up to a poly-log factor) on thc sequential space required by a deterministic Turing machine with an independence oracle to solve the S-search problem.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131801256","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: 12

Factoring with cyclotomic polynomials 用分环多项式分解

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.24

E. Bach, J. Shallit

引用次数: 66