The authors study both the incidence counting and the many-faces problem for various kinds of curves, including lines, pseudolines, unit circles, general circles, and pseudocircles. They also extend the analysis to three dimensions, where they concentrate on the case of spheres, which is relevant for the three-dimensional unit-distance problem. They obtain upper bounds for certain quantities. The authors believe that the techniques they use are of independent interest.<>
{"title":"Combinatorial complexity bounds for arrangements of curves and surfaces","authors":"K. Clarkson, M. Sharir","doi":"10.1109/SFCS.1988.21973","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21973","url":null,"abstract":"The authors study both the incidence counting and the many-faces problem for various kinds of curves, including lines, pseudolines, unit circles, general circles, and pseudocircles. They also extend the analysis to three dimensions, where they concentrate on the case of spheres, which is relevant for the three-dimensional unit-distance problem. They obtain upper bounds for certain quantities. The authors believe that the techniques they use are of independent interest.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129650411","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-cut problem is to find a partition of an edge weighted graph into k nonempty components, such that the total edge weight between components is minimum. This problem is NP-complete for arbitrary k and its version involving fixing a vertex in each component is NP hard even for k=3. A polynomial algorithm for the case of a fixed k is presented.<>
{"title":"Polynomial algorithm for the k-cut problem","authors":"O. Goldschmidt, D. Hochbaum","doi":"10.1109/SFCS.1988.21960","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21960","url":null,"abstract":"The k-cut problem is to find a partition of an edge weighted graph into k nonempty components, such that the total edge weight between components is minimum. This problem is NP-complete for arbitrary k and its version involving fixing a vertex in each component is NP hard even for k=3. A polynomial algorithm for the case of a fixed k is presented.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123715263","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}
An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, >
在任意运算(+，-，/，mod， >)的计算树的深度上证明了(log log n)下界
{"title":"Lower bounds for integer greatest common divisor computations","authors":"Y. Mansour, B. Schieber, Prasoon Tiwari","doi":"10.1145/103516.103522","DOIUrl":"https://doi.org/10.1145/103516.103522","url":null,"abstract":"An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, <or=) that computes the greatest common divisor (GCD) of all pairs of n-bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Theta (n) bound on the depth of any algebraic computation trees with operations (+, -, *, /, <or=) (where \"/\" stands for exact division) that solve many simple problems, e.g. testing if an n-bit integer is odd or computing the GCD of two n-bit integers.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133179585","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}
In one routing scheme which has been implemented on a parallel architecture based on the butterfly graph, messages are sometimes destroyed. It is shown that if messages are sent to random destinations, the expected number of messages that reach their destinations is Theta (n(log n)-1/q), where n is the size of the butterfly graph and q is the number of messages that can move through one edge (or, equivalently, vertex) in one time step. In the analysis of this problem, interesting techniques for solving nonlinear systems of difference equations are developed that could have applications to other problems.<>
{"title":"Increasing the size of a network by a constant factor can increase performance by more than a constant factor","authors":"R.R. Kock","doi":"10.1109/SFCS.1988.21939","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21939","url":null,"abstract":"In one routing scheme which has been implemented on a parallel architecture based on the butterfly graph, messages are sometimes destroyed. It is shown that if messages are sent to random destinations, the expected number of messages that reach their destinations is Theta (n(log n)-1/q), where n is the size of the butterfly graph and q is the number of messages that can move through one edge (or, equivalently, vertex) in one time step. In the analysis of this problem, interesting techniques for solving nonlinear systems of difference equations are developed that could have applications to other problems.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133186551","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 power of various query languages is compared along two dimensions, namely the inherent power of the language and the number of alternations of quantizers. Learning by asking questions is compared to learning by passively reading data. It is found that the extent of what can be learned by queries is largely dependent on the language used by the inference mechanism to formulate questions to ask of its trainer. It is proved that inference machines that are allowed to ask first-order questions with plus and times can be used to solve the halting problem and therefore can learn all the recursive functions. Learning languages are also considered.<>
{"title":"Learning via queries","authors":"W. Gasarch, Carl H. Smith","doi":"10.1109/SFCS.1988.21931","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21931","url":null,"abstract":"The power of various query languages is compared along two dimensions, namely the inherent power of the language and the number of alternations of quantizers. Learning by asking questions is compared to learning by passively reading data. It is found that the extent of what can be learned by queries is largely dependent on the language used by the inference mechanism to formulate questions to ask of its trainer. It is proved that inference machines that are allowed to ask first-order questions with plus and times can be used to solve the halting problem and therefore can learn all the recursive functions. Learning languages are also considered.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133732796","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 authors investigate how good connectivity properties translate into good error-correcting behavior in sparse networks of threshold elements. They determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence in an associative memory model consisting of a sparse network of threshold elements or neurons.<>
{"title":"Effect of connectivity in associative memory models","authors":"J. Komlos, R. Paturi","doi":"10.1109/SFCS.1988.21932","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21932","url":null,"abstract":"The authors investigate how good connectivity properties translate into good error-correcting behavior in sparse networks of threshold elements. They determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence in an associative memory model consisting of a sparse network of threshold elements or neurons.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115809765","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}
A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus g has pagenumber O( square root g); and (2) most n-vertex d-regular graphs have pagenumber Omega ( square root dn/sup 1/2-1/d/).<>
{"title":"Genus g graphs have pagenumber O( square root g)","authors":"S. Malitz","doi":"10.1109/SFCS.1988.21962","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21962","url":null,"abstract":"A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus g has pagenumber O( square root g); and (2) most n-vertex d-regular graphs have pagenumber Omega ( square root dn/sup 1/2-1/d/).<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114619672","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}
A number of important computational problems in molecular biology, geology, speech recognition, and other areas can be expressed as recurrences which have typically been solved with dynamic programming. By using more sophisticated data structures, and by taking advantage of further structure from the applications, the authors speed up the computation of several of these recurrences by one or two orders of magnitude. The algorithms used are simple and practical.<>
{"title":"Speeding up dynamic programming","authors":"D. Eppstein, Z. Galil, R. Giancarlo","doi":"10.1109/SFCS.1988.21965","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21965","url":null,"abstract":"A number of important computational problems in molecular biology, geology, speech recognition, and other areas can be expressed as recurrences which have typically been solved with dynamic programming. By using more sophisticated data structures, and by taking advantage of further structure from the applications, the authors speed up the computation of several of these recurrences by one or two orders of magnitude. The algorithms used are simple and practical.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116928575","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 shown that for directed graphs, reachability can not be expressed by an existential monadic second-order sentence. The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic. However, it is shown that for directed graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence. One reason for the interest in the main result is that while there is considerable empirical evidence (in terms of the efficiency of algorithms that have been discovered) that reachability in directed graphs is 'harder' than reachability in undirected graphs, this is the first proof in a precise technical sense that this is so.<>
{"title":"Reachability is harder for directed than for undirected finite graphs","authors":"M. Ajtai, Ronald Fagin","doi":"10.2307/2274958","DOIUrl":"https://doi.org/10.2307/2274958","url":null,"abstract":"It is shown that for directed graphs, reachability can not be expressed by an existential monadic second-order sentence. The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic. However, it is shown that for directed graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence. One reason for the interest in the main result is that while there is considerable empirical evidence (in terms of the efficiency of algorithms that have been discovered) that reachability in directed graphs is 'harder' than reachability in undirected graphs, this is the first proof in a precise technical sense that this is so.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129820590","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 efficiently performing Byzantine agreement in t+1 rounds in the face of arbitrarily malicious failures is treated. A communication-efficient polynomial-time protocol is presented for n>8t. The protocol is an early stopping protocol, halting in min(t+1, f+2) rounds in the worst case, where f is the number of processors that fail during the run. This is provably optimal. The protocol is based on a careful combination of early stopping, fault masking, and a technique called coordinated traversal. The combination of the three provides a powerful method for restricting the damage that a faulty processor, however malicious, can do. One of the byproducts of this protocol is a polynomial-time (t+1)-round protocol for the Byzantine firing squad problem.<>
{"title":"Coordinated traversal: (t+1)-round Byzantine agreement in polynomial time","authors":"Y. Moses, Orli Waarts","doi":"10.1109/SFCS.1988.21941","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21941","url":null,"abstract":"The problem of efficiently performing Byzantine agreement in t+1 rounds in the face of arbitrarily malicious failures is treated. A communication-efficient polynomial-time protocol is presented for n>8t. The protocol is an early stopping protocol, halting in min(t+1, f+2) rounds in the worst case, where f is the number of processors that fail during the run. This is provably optimal. The protocol is based on a careful combination of early stopping, fault masking, and a technique called coordinated traversal. The combination of the three provides a powerful method for restricting the damage that a faulty processor, however malicious, can do. One of the byproducts of this protocol is a polynomial-time (t+1)-round protocol for the Byzantine firing squad problem.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127444085","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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