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Infinitely-Often Autoreducible Sets 无穷常自约集
SIAM journal on computing (Print) Pub Date : 2003-12-15 DOI: 10.1137/S0097539704441630
R. Beigel, L. Fortnow, F. Stephan
{"title":"Infinitely-Often Autoreducible Sets","authors":"R. Beigel, L. Fortnow, F. Stephan","doi":"10.1137/S0097539704441630","DOIUrl":"https://doi.org/10.1137/S0097539704441630","url":null,"abstract":"A set A is autoreducible if one can compute, for all x, the value A(x) by querying A only at places y ¬= x. Furthermore, A is infinitely-often autoreducible if, for infinitely many x, the value A(x) can be computed by querying A only at places y ¬= x. For all other x, the computation outputs a special symbol to signal that the reduction is undefined. It is shown that for polynomial time Turing and truth-table autoreducibility. there are sets A, B, C in EXP such that A is not infinitely-often Turing autoreducible, B is Turing autoreducible but not infinitely-often truth-table autoreducible, C is truth-table autoreducible with g(n) + 1 queries but not infinitely-often Turing autoreducible with g(n) queries. Here n is the length of the input, g is nondecreasing and there exists a polynomial p such that p(n) bounds both, the computation time and the value, of g at input of length n. Furthermore, connections between notions of infinitely-often autoreducibility and notions of approximability are investigated. The Hausdorff-dimension of the class of sets which are not infinitely-often autoreducible is shown to be 1.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114389939","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: 17
An Optimal Algorithm for the Maximum-Density Segment Problem 最大密度段问题的一种最优算法
SIAM journal on computing (Print) Pub Date : 2003-09-16 DOI: 10.1137/S0097539704440430
Kai-Min Chung, Hsueh-I Lu
{"title":"An Optimal Algorithm for the Maximum-Density Segment Problem","authors":"Kai-Min Chung, Hsueh-I Lu","doi":"10.1137/S0097539704440430","DOIUrl":"https://doi.org/10.1137/S0097539704440430","url":null,"abstract":"We address a fundamental string problem arising from analysis of biomolecular sequences. The input consists of two integers L and U and a sequence S of n number pairs (a i ,w i ) with w i > 0. Let segmentS(i,j) of S be the consecutive subsequence of S starting index i to index j. The density of S(i,j) is d(i,j) = (a i + a i + 1 + ... + a j )/(w i + w i + 1 + ... + w j ). The maximum-density segment problem is to find a maximum-density segment over all segments of S with L ≤ w i + w i + 1 + ... + w j ≤ U. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu, runs in O(n log(U − L + 1)) time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated right-skew decomposition, introduced by Lin, Jiang, and Chao. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences. Moreover, for an input sequence S representable in O(k) space, we also show how to exploit the sparsity of S and solve the maximum-density segment problem for S in O(k) time.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124824799","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: 58
Hardness of Approximation for Vertex-Connectivity Network Design Problems 顶点连通性网络设计问题的逼近硬度
SIAM journal on computing (Print) Pub Date : 2002-09-17 DOI: 10.1137/S0097539702416736
G. Kortsarz, Robert Krauthgamer, James R. Lee
{"title":"Hardness of Approximation for Vertex-Connectivity Network Design Problems","authors":"G. Kortsarz, Robert Krauthgamer, James R. Lee","doi":"10.1137/S0097539702416736","DOIUrl":"https://doi.org/10.1137/S0097539702416736","url":null,"abstract":"In the survivable network design problem SNDP, the goal is to find a minimum-cost subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertexdisjoint paths connecting them.We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient 2log1-?n ratio approximation for any fixed ? > 0 unless NP ? DTIME(npolylog(n)>). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131621633","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: 133
Balanced-Replication Algorithms for Distribution Trees 分布树的均衡复制算法
SIAM journal on computing (Print) Pub Date : 2002-09-17 DOI: 10.1137/S0097539702412143
E. Cohen, Haim Kaplan
{"title":"Balanced-Replication Algorithms for Distribution Trees","authors":"E. Cohen, Haim Kaplan","doi":"10.1137/S0097539702412143","DOIUrl":"https://doi.org/10.1137/S0097539702412143","url":null,"abstract":"In many Internet applications, requests for a certain object are routed bottom-up over a tree where the root of the tree is the node containing the object. When an object becomes popular, the root node of the tree may become a hotspot. Therefore many applications allow intermediate nodes to acquire the ability to serve the requests, for example by caching the object. We call such distinguished nodes primed. We propose and analyse different algorithms where nodes decide when to become primed; these algorithms balance the maximum load on a node and the number of primed nodes. Many applications require both fully distributed decisions and smooth convergence to a stable set of primed nodes. We first present optimal algorithms which require communication across the tree. We then consider the natural previously proposed THRESHOLD algorithm, where a node becomes primed when the incoming flow of requests exceeds a threshold. We show examples where THRESHOLD exhibits undesirable behavior during convergence. Finally, we propose another fully distributed algorithm, GAP, which converges gracefully.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"2017 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114330497","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: 4
On Testing Convexity and Submodularity 关于凸性和子模块性的测试
SIAM journal on computing (Print) Pub Date : 2002-09-13 DOI: 10.1137/S0097539702414026
Michal Parnas, D. Ron, R. Rubinfeld
{"title":"On Testing Convexity and Submodularity","authors":"Michal Parnas, D. Ron, R. Rubinfeld","doi":"10.1137/S0097539702414026","DOIUrl":"https://doi.org/10.1137/S0097539702414026","url":null,"abstract":"Submodular and convex functions play an important role in many applications, and in particular in combinatorial optimization. Here we study two special cases: convexity in one dimension and submodularity in two dimensions. The latter type of functions are equivalent to the well known Monge matrices. A matrix V = {vi,j}i,j=0i=n1, j=n2 is called a Monge matrix if for every 0 ? i < r ? n1 and 0 ? j < s ? n2, we have vi,j + vr,s ? vi,s + vr,j. If inequality holds in the opposite direction then V is an inverse Monge matrix (supermodular function). Many problems, such as the traveling salesperson problem and various transportation problems, can be solved more efficiently if the input is a Monge matrix.In this work we present a testing algorithm for Monge and inverse Monge matrices, whose running time is O ((log n1 ? log n2)/?), where ? is the distance parameter for testing. In addition we have an algorithm that tests whether a function f : [n] ? R is convex (concave) with running time of O ((log n)/?).","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128767469","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: 32
A Second-Order Perceptron Algorithm 二阶感知器算法
SIAM journal on computing (Print) Pub Date : 2002-07-08 DOI: 10.1137/S0097539703432542
N. Cesa-Bianchi, A. Conconi, C. Gentile
{"title":"A Second-Order Perceptron Algorithm","authors":"N. Cesa-Bianchi, A. Conconi, C. Gentile","doi":"10.1137/S0097539703432542","DOIUrl":"https://doi.org/10.1137/S0097539703432542","url":null,"abstract":"We introduce a variant of the Perceptron algorithm called second-order Perceptron algorithm, which is able to exploit certain spectral properties of the data. We analyze the second-order Perceptron algorithm in the mistake bound model of on-line learning and prove bounds in terms of the eigenvalues of the Gram matrix created from the data. The performance of the second-order Perceptron algorithm is affected by the setting of a parameter controlling the sensitivity to the distribution of the eigenvalues of the Gram matrix. Since this information is not preliminarly available to on-line algorithms, we also design a refined version of the second-order Perceptron algorithm which adaptively sets the value of this parameter. For this second algorithm we are able to prove mistake bounds corresponding to a nearly optimal constant setting of the parameter.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117019789","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: 214
Quick k-Median, k-Center, and Facility Location for Sparse Graphs 稀疏图的快速k-Median, k-Center和设施定位
SIAM journal on computing (Print) Pub Date : 2001-07-08 DOI: 10.1137/S0097539701388884
M. Thorup
{"title":"Quick k-Median, k-Center, and Facility Location for Sparse Graphs","authors":"M. Thorup","doi":"10.1137/S0097539701388884","DOIUrl":"https://doi.org/10.1137/S0097539701388884","url":null,"abstract":"Solving an open problem of Jain and Vazirani [FOCS'99], we present O (n+m) time constant factor approximation algorithms for the k-median, k-center, and facility location problems with assignment costs being shortest path distances in a weighted undirected graph with n nodes and m edges. \u0000 \u0000For all of these location problems, O(n2) algorithms were already known, but here we are addressing large sparse graphs. An application could be placement of content distributing servers on the Internet. The Internet is large and changes so frequently that an O(n2) time solution would likely be outdated long before completion.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115035536","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: 99
On the Relationship Between Clique-Width and Treewidth 论团宽与树宽的关系
SIAM journal on computing (Print) Pub Date : 2001-06-14 DOI: 10.1137/S0097539701385351
D. Corneil, Udi Rotics
{"title":"On the Relationship Between Clique-Width and Treewidth","authors":"D. Corneil, Udi Rotics","doi":"10.1137/S0097539701385351","DOIUrl":"https://doi.org/10.1137/S0097539701385351","url":null,"abstract":"Treewidth is generally regarded as one of the most useful parameterizations of a graph's construction. Clique-width is a similar parameterizations that shares one of the powerful properties of treewidth, namely: if a graph is of bounded treewidth (or clique-width), then there is a polynomial time algorithm for any graph problem expressible in Monadic Second Order Logic, using quantifiers on vertices (in the case of clique-width you must assume a clique-width parse expression is given). In studying the relationship between treewidth and clique-width, Courcelle and Olariu showed that any graph of bounded treewidth is also of bounded clique-width; in particular, for any graph G with treewidth k, the clique-width of G ? 4 * 2k-1 + 1.In this paper, we improve this result to the clique-width of G ? 3 * 2k-1 and more importantly show that there is an exponential lower bound on this relationship. In particular, for any k, there is a graph G with treewidth = k where the clique-width of G ? 2?k/2?-1.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123018327","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: 190
Contention Resolution in Hashing Based Shared Memory Simulations 基于散列的共享内存模拟中的争用解决
SIAM journal on computing (Print) Pub Date : 2000-03-01 DOI: 10.1137/S009753979529564X
A. Czumaj, F. Heide, V. Stemann
{"title":"Contention Resolution in Hashing Based Shared Memory Simulations","authors":"A. Czumaj, F. Heide, V. Stemann","doi":"10.1137/S009753979529564X","DOIUrl":"https://doi.org/10.1137/S009753979529564X","url":null,"abstract":"In this paper we study the problem of simulating shared memory on the distributed memory machine (DMM). Our approach uses multiple copies of shared memory cells, distributed among the memory modules of the DMM via universal hashing. The main aim is to design strategies that resolve contention at the memory modules. Extending results and methods from random graphs and very fast randomized algorithms, we present new simulation techniques that enable us to improve the previously best results exponentially. In particular, we show that an $n$-processor CRCW PRAM can be simulated by an n-processor DMM with delay $O(logloglog n log^*n)$, with high probability. \u0000Next we describe a general technique that can be used to turn these simulations into time-processor optimal ones, in the case of EREW PRAMs to be simulated. We obtain a time-processor optimal simulation of an (n log log log n log*n)-processor EREW PRAM on an n-processor DMM with delay $O(logloglog n log^*n)$, with high probability. When an (n log log log n log*n)-processor CRCW PRAM is simulated, the delay is only by a log*n factor larger. \u0000We further demonstrate that the simulations presented can not be significantly improved using our techniques. We show an $Omega(logloglog n / loglogloglog n)$ lower bound on the expected delay for a class of PRAM simulations, called topological simulations, that covers all previously known simulations as well as the simulations presented in the paper.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126628037","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: 22
General Multiprocessor Task Scheduling: Approximate Solutions in Linear Time 通用多处理器任务调度:线性时间的近似解
SIAM journal on computing (Print) Pub Date : 1999-08-11 DOI: 10.1137/S0097539799361737
K. Jansen, L. Porkolab
{"title":"General Multiprocessor Task Scheduling: Approximate Solutions in Linear Time","authors":"K. Jansen, L. Porkolab","doi":"10.1137/S0097539799361737","DOIUrl":"https://doi.org/10.1137/S0097539799361737","url":null,"abstract":"We study the problem of scheduling a set of n independent tasks on a fixed number of parallel processors, where the execution time of a task is a function of the subset of processors assigned to the task. We propose a fully polynomial approximation scheme that for any fixed Ɛ > 0 finds a preemptive schedule of length at most (1 + Ɛ) times the optimum in O(n) time. We also discuss the non-preemptive variant of the problem, and present a polynomial approximation scheme that computes an approximate solution of any fixed accuracy in linear time. In terms of the running time, this linear complexity bound gives a substantial improvement of the best previously known polynomial bound [5].","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133785997","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: 27
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