The technique of speeding up access into search structures by maintaining fingers that point to various locations of the search structure is considered. The problem of choosing, in a large search structure, locations at which to maintain fingers is treated. In particular, a server problem in which k servers move along a line segment of length m, where m is the number of keys in the search structure, is addressed. Since fingers may be arbitrarily copied, a server is allowed to jump, or fork, to a location currently occupied by another server. Online algorithms are presented and their competitiveness analyzed. It is shown that the case in which k=2 behaves differently from the case in which k>or=3, by showing that there is a four-competitive algorithm for k=2 that never forks its fingers. For k>or=3, it is shown that any online algorithm that does not fork its fingers can be at most Omega (m/sup 1/2/)-competitive. The main result is that for k=3 there is an online algorithm that forks and is constant competitive (independent of m, the size of the search structure). The algorithm is simple and implementable.<>
{"title":"Online algorithms for finger searching","authors":"Richard Cole, A. Raghunathan","doi":"10.1109/FSCS.1990.89569","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89569","url":null,"abstract":"The technique of speeding up access into search structures by maintaining fingers that point to various locations of the search structure is considered. The problem of choosing, in a large search structure, locations at which to maintain fingers is treated. In particular, a server problem in which k servers move along a line segment of length m, where m is the number of keys in the search structure, is addressed. Since fingers may be arbitrarily copied, a server is allowed to jump, or fork, to a location currently occupied by another server. Online algorithms are presented and their competitiveness analyzed. It is shown that the case in which k=2 behaves differently from the case in which k>or=3, by showing that there is a four-competitive algorithm for k=2 that never forks its fingers. For k>or=3, it is shown that any online algorithm that does not fork its fingers can be at most Omega (m/sup 1/2/)-competitive. The main result is that for k=3 there is an online algorithm that forks and is constant competitive (independent of m, the size of the search structure). The algorithm is simple and implementable.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123871724","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}
Several tools for use in approximation algorithms to color 3-chromatic graphs are presented. The techniques are used in an algorithm that colors any 3-chromatic graph with O(n/sup 3/8/)+O(n/sup 3/8+O(1)/) colors (or more precisely) O(n/sup 3/8/log/sup 5/8/ n) colors, which improves the previous best bound of O(n/sup 0.4+0(1)/) colors. The techniques are illustrated by considering a problem in which the 3-chromatic graph is created not by a worst-case adversary, but by an adversary each of whose decisions (whether or not to include an edge) is reversed with some small probability or noise rate p. This type of adversary is equivalent to the semirandom source of M. Santha and U.V. Vazirani (1986). An algorithm that will actually 3-color such a graph with high probability even for quite low noise rates (p>or=n/sup -1/2+ epsilon / for constant epsilon >0), is presented.<>
{"title":"Some tools for approximate 3-coloring","authors":"Avrim Blum","doi":"10.1109/FSCS.1990.89576","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89576","url":null,"abstract":"Several tools for use in approximation algorithms to color 3-chromatic graphs are presented. The techniques are used in an algorithm that colors any 3-chromatic graph with O(n/sup 3/8/)+O(n/sup 3/8+O(1)/) colors (or more precisely) O(n/sup 3/8/log/sup 5/8/ n) colors, which improves the previous best bound of O(n/sup 0.4+0(1)/) colors. The techniques are illustrated by considering a problem in which the 3-chromatic graph is created not by a worst-case adversary, but by an adversary each of whose decisions (whether or not to include an edge) is reversed with some small probability or noise rate p. This type of adversary is equivalent to the semirandom source of M. Santha and U.V. Vazirani (1986). An algorithm that will actually 3-color such a graph with high probability even for quite low noise rates (p>or=n/sup -1/2+ epsilon / for constant epsilon >0), is presented.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124985052","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}
Motivated by, the problem of understanding the limitations of neural networks for representing Boolean functions, the authors consider size-depth tradeoffs for threshold circuits that compute the parity function. They give an almost optimal lower bound on the number of edges of any depth-2 threshold circuit that computes the parity function with polynomially bounded weights. The main technique used in the proof, which is based on the theory of rational approximation, appears to be a potentially useful technique for the analysis of such networks. It is conjectured that there are no linear size, bounded-depth threshold circuits for computing parity.<>
{"title":"On threshold circuits for parity","authors":"R. Paturi, M. Saks","doi":"10.1109/FSCS.1990.89559","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89559","url":null,"abstract":"Motivated by, the problem of understanding the limitations of neural networks for representing Boolean functions, the authors consider size-depth tradeoffs for threshold circuits that compute the parity function. They give an almost optimal lower bound on the number of edges of any depth-2 threshold circuit that computes the parity function with polynomially bounded weights. The main technique used in the proof, which is based on the theory of rational approximation, appears to be a potentially useful technique for the analysis of such networks. It is conjectured that there are no linear size, bounded-depth threshold circuits for computing parity.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"360 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122767838","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}
L. Babai, G. Hetyei, W. Kantor, A. Lubotzky, Á. Seress
The diameter of a group G with respect to a set S of generators is the maximum over g in G of the length of the shortest word in S union S/sup -1/ representing g. This concept arises in the contexts of efficient communication networks and Rubik's-cube-type puzzles. 'Best' generators are pertinent to networks, whereas 'worst' and 'average' generators seem more adequate models for puzzles. A substantial body of recent work on these subjects by the authors is surveyed. Regarding the 'best' case, it is shown that, although the structure of the group is essentially irrelevant if mod S mod is allowed to exceed (log mod G mod )/sup 1+c/(c>0), it plays a strong role when mod S mod =O(1).<>
群G相对于集合S的生成器的直径是G中S并集S/sup -1/表示G的最短单词的长度在G上的最大值。这个概念出现在有效的通信网络和魔方类型的谜题中。“最佳”生成器与网络相关，而“最差”和“一般”生成器似乎更适合解谜。作者对这些主题最近的大量工作进行了调查。对于“最佳”情况，我们发现，尽管在允许mod S mod超过(log mod G mod)/sup 1+c/(c>0)的情况下，群的结构本质上是无关紧要的，但当mod S mod =O(1)时，群的结构起着很强的作用。
{"title":"On the diameter of finite groups","authors":"L. Babai, G. Hetyei, W. Kantor, A. Lubotzky, Á. Seress","doi":"10.1109/FSCS.1990.89608","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89608","url":null,"abstract":"The diameter of a group G with respect to a set S of generators is the maximum over g in G of the length of the shortest word in S union S/sup -1/ representing g. This concept arises in the contexts of efficient communication networks and Rubik's-cube-type puzzles. 'Best' generators are pertinent to networks, whereas 'worst' and 'average' generators seem more adequate models for puzzles. A substantial body of recent work on these subjects by the authors is surveyed. Regarding the 'best' case, it is shown that, although the structure of the group is essentially irrelevant if mod S mod is allowed to exceed (log mod G mod )/sup 1+c/(c>0), it plays a strong role when mod S mod =O(1).<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114543507","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}
Michael Formann, T. Hagerup, J. Haralambides, Michael Kaufmann, F. Leighton, A. Symvonis, E. Welzl, G. Woeginger
The problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized is studied. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph is defined to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that Omega (1/d/sup 2/)>
{"title":"Drawing graphs in the plane with high resolution","authors":"Michael Formann, T. Hagerup, J. Haralambides, Michael Kaufmann, F. Leighton, A. Symvonis, E. Welzl, G. Woeginger","doi":"10.1109/FSCS.1990.89527","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89527","url":null,"abstract":"The problem of drawing a graph in the plane so that edges appear as straight lines and the minimum angle formed by any pair of incident edges is maximized is studied. The resolution of a layout is defined to be the size of the minimum angle formed by incident edges of the graph, and the resolution of a graph is defined to be the maximum resolution of any layout of the graph. The resolution R of a graph is characterized in terms of the maximum node degree d of the graph by proving that Omega (1/d/sup 2/)<or=R<or=2 pi /d for any graph. Moreover, it is proved that R= Theta (1/d) for many graphs, including planar graphs, complete graphs, hypercubes, multidimensional meshes and tori, and other special networks. It is also shown that the problem of deciding if R=2 pi /d for a graph is NP-hard for d=4, and a counting argument is used to show that R=O(log d/d/sup 2/) for many graphs.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114603313","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}
B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink
A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered.<>
{"title":"Counting and cutting cycles of lines and rods in space","authors":"B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink","doi":"10.1109/FSCS.1990.89543","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89543","url":null,"abstract":"A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129038669","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}
It is proved that for every c<1 there are perfect-information coin-flipping and leader-election games on n players in which no coalition of cn players can influence the outcome with probability greater than some universal constant times c. It is shown that a random protocol of a certain length has this property, and an explicit construction is given as well.<>
证明了对于每一个c>
{"title":"Coin-flipping games immune against linear-sized coalitions","authors":"N. Alon, M. Naor","doi":"10.1109/FSCS.1990.89523","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89523","url":null,"abstract":"It is proved that for every c<1 there are perfect-information coin-flipping and leader-election games on n players in which no coalition of cn players can influence the outcome with probability greater than some universal constant times c. It is shown that a random protocol of a certain length has this property, and an explicit construction is given as well.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121507703","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}
The problem of deciding the validity of formulas in extensions of propositional dynamic logic (PDL) is considered. The extensions are obtained by adding programs defined by nonregular languages. In the past, a number of very simple languages were shown to render this problem highly undecidable, whereas other very similar-looking languages were shown to retain decidability. Understanding this rather strange phenomenon and generalizing the isolated extensions have remained elusive. The authors provide decision procedures for two wide classes of extensions, thus shedding light on the general problem. The proofs are novel, in that they explicitly consider the machines that accept the languages, in this case special classes of PDAs and stack automata. It is shown that the emptiness problem for stack automata on infinite trees is decidable, a result of independent interest, and the result is combined with the construction of certain tree models for the corresponding formulas.<>
{"title":"Deciding properties of nonregular programs","authors":"D. Harel, D. Raz","doi":"10.1109/FSCS.1990.89587","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89587","url":null,"abstract":"The problem of deciding the validity of formulas in extensions of propositional dynamic logic (PDL) is considered. The extensions are obtained by adding programs defined by nonregular languages. In the past, a number of very simple languages were shown to render this problem highly undecidable, whereas other very similar-looking languages were shown to retain decidability. Understanding this rather strange phenomenon and generalizing the isolated extensions have remained elusive. The authors provide decision procedures for two wide classes of extensions, thus shedding light on the general problem. The proofs are novel, in that they explicitly consider the machines that accept the languages, in this case special classes of PDAs and stack automata. It is shown that the emptiness problem for stack automata on infinite trees is decidable, a result of independent interest, and the result is combined with the construction of certain tree models for the corresponding formulas.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121631633","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}
The parallel complexity of solving linear programming problems is studied in the context of interior point methods. If n and m, respectively, denote the number of variables and the number of constraints in the given problem, an algorithm that solves linear programming problems in O((mn)/sup 1/4/ (log 1 n)/sup 3/L) time using O(M(n)m/n+1n/sup 3/) processors is given. (M(n) is the number of operations for multiplying two n*n matrices). This gives an improvement in the parallel running time for n=o(m). A typical case in which n=o(m) is the dual of the uncapacitated transportation problem. The algorithm solves the uncapacitated transportation problem in O((VE)/sup 1/4/(log V)/sup 3/ (log V gamma )) time using O(V/sup 3/) processors, where V (E) is the number of nodes (edges) and gamma is the largest magnitude of an edge cost or a demand at a node. As a by-product, a better parallel algorithm for the assignment problem for graphs of moderate density is obtained.<>
{"title":"Reducing the parallel complexity of certain linear programming problems","authors":"P. M. Vaidya","doi":"10.1109/FSCS.1990.89579","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89579","url":null,"abstract":"The parallel complexity of solving linear programming problems is studied in the context of interior point methods. If n and m, respectively, denote the number of variables and the number of constraints in the given problem, an algorithm that solves linear programming problems in O((mn)/sup 1/4/ (log 1 n)/sup 3/L) time using O(M(n)m/n+1n/sup 3/) processors is given. (M(n) is the number of operations for multiplying two n*n matrices). This gives an improvement in the parallel running time for n=o(m). A typical case in which n=o(m) is the dual of the uncapacitated transportation problem. The algorithm solves the uncapacitated transportation problem in O((VE)/sup 1/4/(log V)/sup 3/ (log V gamma )) time using O(V/sup 3/) processors, where V (E) is the number of nodes (edges) and gamma is the largest magnitude of an edge cost or a demand at a node. As a by-product, a better parallel algorithm for the assignment problem for graphs of moderate density is obtained.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131989485","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}
The k differences approximate string matching problem specifies a text string of length n, a pattern string of length m, and the number k of differences (insertions, deletions, substitutions) allowed in a match, and asks for every location in the text where a match occurs. Previous algorithms required at least O(nk) time. When k is as large as a fraction of m, no substantial progress has been made over O(nm) dynamic programming. The authors have investigated much faster algorithms for restricted cases of the problem, such as when the text string is random and errors are not too frequent. They have devised an algorithm that, for k>
{"title":"Approximate string matching in sublinear expected time","authors":"W. I. Chang, E. Lawler","doi":"10.1109/FSCS.1990.89530","DOIUrl":"https://doi.org/10.1109/FSCS.1990.89530","url":null,"abstract":"The k differences approximate string matching problem specifies a text string of length n, a pattern string of length m, and the number k of differences (insertions, deletions, substitutions) allowed in a match, and asks for every location in the text where a match occurs. Previous algorithms required at least O(nk) time. When k is as large as a fraction of m, no substantial progress has been made over O(nm) dynamic programming. The authors have investigated much faster algorithms for restricted cases of the problem, such as when the text string is random and errors are not too frequent. They have devised an algorithm that, for k<m/log n+O(1), runs in time O((n/m)k log n) on the average. In the worst case their algorithm is O(nk), but it is still an improvement in that it is very practical and uses only O(n) space compared with O(n) or O(n/sup 2/). The authors define an approximate substring matching problem and give efficient algorithms based on their techniques. Special cases include several applications to genetics and molecular biology.<<ETX>>","PeriodicalId":271949,"journal":{"name":"Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130979374","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}
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