Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185400
H. Edelsbrunner, T. Tan
It is shown that a triangulation of a set of n points in the plane that minimizes the maximum edge length can be computed in time O(n/sup 2/). The algorithm is reasonably easy to implement and is based on the theorem that there is a triangulation with minmax edge length that contains the relative neighborhood graph of the points as a subgraph. With minor modifications the algorithm works for arbitrary normed metrics.<>
{"title":"A quadratic time algorithm for the minmax length triangulation","authors":"H. Edelsbrunner, T. Tan","doi":"10.1109/SFCS.1991.185400","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185400","url":null,"abstract":"It is shown that a triangulation of a set of n points in the plane that minimizes the maximum edge length can be computed in time O(n/sup 2/). The algorithm is reasonably easy to implement and is based on the theorem that there is a triangulation with minmax edge length that contains the relative neighborhood graph of the points as a subgraph. With minor modifications the algorithm works for arbitrary normed metrics.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"400 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115988573","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185364
I-Chen Wu, H. T. Kung
The relationship between parallel computation cost and communication cost for performing divide-and-conquer (D&C) computations on a parallel system of p processors is studied. The parallel computation cost is the maximal number of the D&C nodes that any processor in the parallel system may expand, whereas the communication cost is the total number of cross nodes (nodes generated by one processor but expanded by another processor). A scheduling algorithm is proposed, and lower bounds on the communication cost are derived. The proposed scheduling algorithm is optimal with respect to the communication cost, since the parallel computation cost of the algorithm is near optimal.<>
{"title":"Communication complexity for parallel divide-and-conquer","authors":"I-Chen Wu, H. T. Kung","doi":"10.1109/SFCS.1991.185364","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185364","url":null,"abstract":"The relationship between parallel computation cost and communication cost for performing divide-and-conquer (D&C) computations on a parallel system of p processors is studied. The parallel computation cost is the maximal number of the D&C nodes that any processor in the parallel system may expand, whereas the communication cost is the total number of cross nodes (nodes generated by one processor but expanded by another processor). A scheduling algorithm is proposed, and lower bounds on the communication cost are derived. The proposed scheduling algorithm is optimal with respect to the communication cost, since the parallel computation cost of the algorithm is near optimal.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"206 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128405811","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185447
W. Maass, G. Schnitger, Eduardo Sontag
The power of constant depth circuits with sigmoid (i.e., smooth) threshold gates for computing Boolean functions is examined. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size Boolean threshold circuits (i.e., circuits with Boolean threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same Boolean functions as the corresponding circuits with Boolean threshold gates.<>
{"title":"On the computational power of sigmoid versus Boolean threshold circuits","authors":"W. Maass, G. Schnitger, Eduardo Sontag","doi":"10.1109/SFCS.1991.185447","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185447","url":null,"abstract":"The power of constant depth circuits with sigmoid (i.e., smooth) threshold gates for computing Boolean functions is examined. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size Boolean threshold circuits (i.e., circuits with Boolean threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same Boolean functions as the corresponding circuits with Boolean threshold gates.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"57 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132569691","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185378
B. Awerbuch, B. Patt-Shamir, G. Varghese
The first self-stabilizing end-to-end communication protocol and the most efficient known self-stabilizing network reset protocol are introduced. A simple method of local checking and correction, by which distributed protocols can be made self-stabilizing without the use of unbounded counters, is used. The self-stabilization model distinguishes between catastrophic faults that abstract arbitrary corruption of global state, and other restricted kinds of anticipated faults. It is assumed that after the execution starts there are no further catastrophic faults, but the anticipated faults may continue to occur.<>
{"title":"Self-stabilization by local checking and correction","authors":"B. Awerbuch, B. Patt-Shamir, G. Varghese","doi":"10.1109/SFCS.1991.185378","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185378","url":null,"abstract":"The first self-stabilizing end-to-end communication protocol and the most efficient known self-stabilizing network reset protocol are introduced. A simple method of local checking and correction, by which distributed protocols can be made self-stabilizing without the use of unbounded counters, is used. The self-stabilization model distinguishes between catastrophic faults that abstract arbitrary corruption of global state, and other restricted kinds of anticipated faults. It is assumed that after the execution starts there are no further catastrophic faults, but the anticipated faults may continue to occur.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122641753","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185345
B. Chazelle
An optimal algorithm for computing hyperplane cuttings is given. It results in a new kind of cutting, which enjoys all the properties of the previous ones and, in addition, can be refined by composition. An optimal algorithm for computing the convex hull of a finite point set in any fixed dimension is also given.<>
{"title":"An optimal convex hull algorithm and new results on cuttings","authors":"B. Chazelle","doi":"10.1109/SFCS.1991.185345","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185345","url":null,"abstract":"An optimal algorithm for computing hyperplane cuttings is given. It results in a new kind of cutting, which enjoys all the properties of the previous ones and, in addition, can be refined by composition. An optimal algorithm for computing the convex hull of a finite point set in any fixed dimension is also given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121830226","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185405
Oded Goldreich, S. Goldwasser, N. Linial
Efficient two-party protocols for fault-tolerant computation of any two-argument function are presented. It is proved that the influence of a dishonest player in these protocols is the minimum one possible (up to polylogarithmic factors). Also presented are efficient m-party fault-tolerant protocols for sampling a general distribution (m>or=2). Efficient m-party protocols for computation of any m-argument function are given, and it is proved for these protocols that for most functions, the influence of any t dishonest players on the outcome of the protocol is the minimum one possible (up to polylogarithmic factors).<>
{"title":"Fault-tolerant computation in the full information model","authors":"Oded Goldreich, S. Goldwasser, N. Linial","doi":"10.1109/SFCS.1991.185405","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185405","url":null,"abstract":"Efficient two-party protocols for fault-tolerant computation of any two-argument function are presented. It is proved that the influence of a dishonest player in these protocols is the minimum one possible (up to polylogarithmic factors). Also presented are efficient m-party fault-tolerant protocols for sampling a general distribution (m>or=2). Efficient m-party protocols for computation of any m-argument function are given, and it is proved for these protocols that for most functions, the influence of any t dishonest players on the outcome of the protocol is the minimum one possible (up to polylogarithmic factors).<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117316268","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185365
C. Papadimitriou
The complexity of certain natural generalizations of satisfiability, in which one of the possibly exponentially many satisfying truth assignments must be selected, is studied. Two natural selection criteria, default preference and minimality (circumscription), are considered. The thrust of the complexity results seems to be that hard problems become harder, while easy problems remain easy. This consideration yields as a byproduct a new and very natural polynomial-time randomized algorithm for 2SAT.<>
{"title":"On selecting a satisfying truth assignment","authors":"C. Papadimitriou","doi":"10.1109/SFCS.1991.185365","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185365","url":null,"abstract":"The complexity of certain natural generalizations of satisfiability, in which one of the possibly exponentially many satisfying truth assignments must be selected, is studied. Two natural selection criteria, default preference and minimality (circumscription), are considered. The thrust of the complexity results seems to be that hard problems become harder, while easy problems remain easy. This consideration yields as a byproduct a new and very natural polynomial-time randomized algorithm for 2SAT.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128407461","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 communication complexity of zero-knowledge proof systems is improved. Let C be a Boolean circuit of size n. Previous zero-knowledge proof systems for the satisfiability of C require the use of Omega (kn) bit commitments in order to achieve a probability of undetected cheating not greater than 2/sup -k/. In the case k=n, the communication complexity of these protocols is therefore Omega (n/sup 2/) bit commitments. A zero-knowledge proof is given for achieving the same goal with only O(n/sup m/+k square root n/sup m/) bit commitments, where m=1+ epsilon /sub n/ and epsilon /sub n/ goes to zero as n goes to infinity. In the case k=n, this is O(n square root n/sup m/). Moreover, only O(k) commitments need ever be opened, which is interesting if committing to a bit is significantly less expensive than opening a commitment.<>
{"title":"Subquadratic zero-knowledge","authors":"J. Boyar, G. Brassard, R. Peralta","doi":"10.1145/227683.227686","DOIUrl":"https://doi.org/10.1145/227683.227686","url":null,"abstract":"The communication complexity of zero-knowledge proof systems is improved. Let C be a Boolean circuit of size n. Previous zero-knowledge proof systems for the satisfiability of C require the use of Omega (kn) bit commitments in order to achieve a probability of undetected cheating not greater than 2/sup -k/. In the case k=n, the communication complexity of these protocols is therefore Omega (n/sup 2/) bit commitments. A zero-knowledge proof is given for achieving the same goal with only O(n/sup m/+k square root n/sup m/) bit commitments, where m=1+ epsilon /sub n/ and epsilon /sub n/ goes to zero as n goes to infinity. In the case k=n, this is O(n square root n/sup m/). Moreover, only O(k) commitments need ever be opened, which is interesting if committing to a bit is significantly less expensive than opening a commitment.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124755473","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185442
L. Babai, K. Friedl
The asymptotic stability and complexity of floating point manipulation of representations of a finite group G are considered, especially splitting them into irreducible constituents and deciding their equivalence. Using rapid mixing estimates for random walks, the authors analyze a classical algorithm by J. Dixon (1970). They find that both its stability and complexity critically depend on the diameter d=diam(G,S) (S is the set that generates G). They propose a worst-case speedup by using Erdos-Renyi generators and modifying the Dixon averaging method. The overall effect in asymptotic complexity is a guaranteed (n log mod G mod )/sup O(1)/ running time.<>
研究了有限群G表示的浮点操作的渐近稳定性和复杂性，特别是将它们分割成不可约的成分并确定它们的等价性。作者利用随机漫步的快速混合估计，分析了J. Dixon(1970)的经典算法。他们发现其稳定性和复杂性都严重依赖于直径d=直径(G,S) (S是产生G的集合)。他们提出了使用Erdos-Renyi生成器和修改Dixon平均方法的最坏情况加速。在渐近复杂度方面的总体效果是保证(n log mod G mod)/sup O(1)/运行时间
{"title":"Approximate representation theory of finite groups","authors":"L. Babai, K. Friedl","doi":"10.1109/SFCS.1991.185442","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185442","url":null,"abstract":"The asymptotic stability and complexity of floating point manipulation of representations of a finite group G are considered, especially splitting them into irreducible constituents and deciding their equivalence. Using rapid mixing estimates for random walks, the authors analyze a classical algorithm by J. Dixon (1970). They find that both its stability and complexity critically depend on the diameter d=diam(G,S) (S is the set that generates G). They propose a worst-case speedup by using Erdos-Renyi generators and modifying the Dixon averaging method. The overall effect in asymptotic complexity is a guaranteed (n log mod G mod )/sup O(1)/ running time.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"176 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129480260","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185397
N. Kahalé
The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.<>
{"title":"Better expansion for Ramanujan graphs","authors":"N. Kahalé","doi":"10.1109/SFCS.1991.185397","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185397","url":null,"abstract":"The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117351414","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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