Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185373
A. Orlitsky
Suppose (X,Y) is a pair of random variables distributed over a support set S. Person P/sub x/ knows X, person P/sub y/ knows Y, and both know S. Using a predetermined protocol, they exchange binary messages in order for P/sub y/ to learn X. P/sub x/ may or may not learn Y. Bounds on communication complexity are obtained and used to obtain efficient protocols for the correlated files problem where X and Y are binary strings (files) within a small edit distance from each other. The average number of bits required for P/sub y/ to learn X when at most m messages are permitted is also determined.<>
假设(X, Y)是两个随机变量分布在一组支持美国人P /子/知道X, P /子Y / Y,知道的人都知道美国使用一个预先确定的协议,他们交换二进制消息为了P / sub X Y /学习/ sub X /可能会或可能不会得到学习Y .界限沟通的复杂性和用于获得有效协议的相关文件问题,X和Y是二进制字符串(文件)在一个小的编辑距离。当最多允许m个消息时，P/sub y/学习X所需的平均位数也被确定。
{"title":"Interactive communication: balanced distributions, correlated files, and average-case complexity","authors":"A. Orlitsky","doi":"10.1109/SFCS.1991.185373","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185373","url":null,"abstract":"Suppose (X,Y) is a pair of random variables distributed over a support set S. Person P/sub x/ knows X, person P/sub y/ knows Y, and both know S. Using a predetermined protocol, they exchange binary messages in order for P/sub y/ to learn X. P/sub x/ may or may not learn Y. Bounds on communication complexity are obtained and used to obtain efficient protocols for the correlated files problem where X and Y are binary strings (files) within a small edit distance from each other. The average number of bits required for P/sub y/ to learn X when at most m messages are permitted is also determined.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"26 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":"125595422","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.1991.185382
Xiaotie Deng, T. Kameda, C. Papadimitriou
The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter offline problem (optimally verifying a map) is NP-hard and thus must be solved approximately. Although the authors show that there is no such competitive algorithm for general obstacle courses, they give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it.<>
{"title":"How to learn an unknown environment","authors":"Xiaotie Deng, T. Kameda, C. Papadimitriou","doi":"10.1109/SFCS.1991.185382","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185382","url":null,"abstract":"The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter offline problem (optimally verifying a map) is NP-hard and thus must be solved approximately. Although the authors show that there is no such competitive algorithm for general obstacle courses, they give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"4 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":"128538382","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.1991.185427
R. Sundar
A fundamental open question in data structures concerns the existence of a dictionary data structure that processes the operations in constant amortized time and uses space polynomial in the dictionary size. The complexity of the dictionary problem is studied under a multilevel hashing model that is based on A.C. Yao's (1981) cell probe model, and it is proved that dictionary operations require log-algorithmic amortized time jn this model. The model encompasses many known solutions to the dictionary problem, and the result is the first nontrivial lower bound for the problem in a reasonably general model that takes into account the limited wordsize of memory locations and realistically measures the cost of update operations. This lower bound separates the deterministic and randomized complexities of the problem under this model.<>
{"title":"A lower bound for the dictionary problem under a hashing model","authors":"R. Sundar","doi":"10.1109/SFCS.1991.185427","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185427","url":null,"abstract":"A fundamental open question in data structures concerns the existence of a dictionary data structure that processes the operations in constant amortized time and uses space polynomial in the dictionary size. The complexity of the dictionary problem is studied under a multilevel hashing model that is based on A.C. Yao's (1981) cell probe model, and it is proved that dictionary operations require log-algorithmic amortized time jn this model. The model encompasses many known solutions to the dictionary problem, and the result is the first nontrivial lower bound for the problem in a reasonably general model that takes into account the limited wordsize of memory locations and realistically measures the cost of update operations. This lower bound separates the deterministic and randomized complexities of the problem under this model.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"2 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":"129175327","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.1991.185369
O. Schwarzkopf
The problem of dynamically maintaining geometric structures is considered. A technique is proposed that uses randomized incremental algorithms which are augmented to allow deletions of objects. A model for distributions on the possible input sequences of insertions and deletions is developed and analyzed using R. Seidel's backwards analysis. It is further shown how to apply this to maintain Voronoi diagrams, convex hulls, and planar subdivisions. A strikingly simple algorithm for the maintenance of convex hulls in any dimension is given. The expected running time is determined.<>
{"title":"Dynamic maintenance of geometric structures made easy","authors":"O. Schwarzkopf","doi":"10.1109/SFCS.1991.185369","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185369","url":null,"abstract":"The problem of dynamically maintaining geometric structures is considered. A technique is proposed that uses randomized incremental algorithms which are augmented to allow deletions of objects. A model for distributions on the possible input sequences of insertions and deletions is developed and analyzed using R. Seidel's backwards analysis. It is further shown how to apply this to maintain Voronoi diagrams, convex hulls, and planar subdivisions. A strikingly simple algorithm for the maintenance of convex hulls in any dimension is given. The expected running time is determined.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"17 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":"114354661","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.1991.185343
R. Beigel, M. Bellare, J. Feigenbaum, S. Goldwasser
Languages in NP are presented for which it is harder to prove membership interactively than it is to decide this membership. Similarly, languages where checking is harder than computing membership are presented. Under assumptions about triple-exponential time, incoherent sets in NP are constructed. Without any assumptions, incoherent sets are constructed in DSPACE (n to the log n), yielding the first uncheckable and non-random-self-reducible sets in that space.<>
{"title":"Languages that are easier than their proofs","authors":"R. Beigel, M. Bellare, J. Feigenbaum, S. Goldwasser","doi":"10.1109/SFCS.1991.185343","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185343","url":null,"abstract":"Languages in NP are presented for which it is harder to prove membership interactively than it is to decide this membership. Similarly, languages where checking is harder than computing membership are presented. Under assumptions about triple-exponential time, incoherent sets in NP are constructed. Without any assumptions, incoherent sets are constructed in DSPACE (n to the log n), yielding the first uncheckable and non-random-self-reducible sets in that space.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"25 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":"128110001","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.1991.185452
Arvind Gupta, R. Impagliazzo
The proof of Wagner's conjecture by N. Robertson and P. Seymour gives a finite description of any family of graphs which is closed under the minor ordering, called the obstructions of the family. Since the intersection and the union of two minor closed graph families are again a minor closed graph family, an interesting question is that of computing the obstructions of the new family given the obstructions for the original two families. It is easy to compute the obstructions of the intersection, but, until very recently, it was an open problem to compute the obstructions of the union. It is shown that if the original families are planar, then the obstructions of the union are no larger than n to the O(n/sup 2/) power, where n is the size of the largest obstruction of the original family.<>
N. Robertson和P. Seymour对Wagner猜想的证明给出了在小序下封闭的任何图族的有限描述，这些图族被称为族的阻碍。由于两个小封闭图族的交集和并集又是一个小封闭图族，一个有趣的问题是在给定原两个小封闭图族的阻碍的情况下计算新族的阻碍。计算交集的障碍物很容易，但是，直到最近，计算并集的障碍物还是一个开放的问题。结果表明，如果原族是平面的，则联合的障碍不大于n的O(n/sup 2/)次方，其中n为原族最大障碍的大小。
{"title":"Computing planar intertwines","authors":"Arvind Gupta, R. Impagliazzo","doi":"10.1109/SFCS.1991.185452","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185452","url":null,"abstract":"The proof of Wagner's conjecture by N. Robertson and P. Seymour gives a finite description of any family of graphs which is closed under the minor ordering, called the obstructions of the family. Since the intersection and the union of two minor closed graph families are again a minor closed graph family, an interesting question is that of computing the obstructions of the new family given the obstructions for the original two families. It is easy to compute the obstructions of the intersection, but, until very recently, it was an open problem to compute the obstructions of the union. It is shown that if the original families are planar, then the obstructions of the union are no larger than n to the O(n/sup 2/) power, where n is the size of the largest obstruction of the original family.<<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":"131819980","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.1991.185419
David R Karger, D. Koller, S. Phillips
The all-pairs shortest paths problem in weighted graphs is investigated. An algorithm called the hidden paths algorithm, which finds these paths in time O(m*+n n/sup 2/ log n), where m* is the number of edges participating in shortest paths, is presented. It is argued that m* is likely to be small in practice, since m*=O(n log n) with high probability for many probability distributions on edge weights. An Omega (mn) lower bound on the running time of any path-comparison-based algorithm for the all-pairs shortest paths problem is proved.<>
{"title":"Finding the hidden path: time bounds for all-pairs shortest paths","authors":"David R Karger, D. Koller, S. Phillips","doi":"10.1109/SFCS.1991.185419","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185419","url":null,"abstract":"The all-pairs shortest paths problem in weighted graphs is investigated. An algorithm called the hidden paths algorithm, which finds these paths in time O(m*+n n/sup 2/ log n), where m* is the number of edges participating in shortest paths, is presented. It is argued that m* is likely to be small in practice, since m*=O(n log n) with high probability for many probability distributions on edge weights. An Omega (mn) lower bound on the running time of any path-comparison-based algorithm for the all-pairs shortest paths problem is proved.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"120 1 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":"124511847","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.1991.185432
B. Donald, Davied Renpan Chang
An algorithm for computing the homology type of a triangulation is analyzed. By triangulation is meant a finite simplicial complex; its homology type is given by its homology groups (with integer coefficients). The algorithm could be used in computer-aided design to tell whether two finite-element meshes or Bezier-spline surfaces are of the same topological type, and whether they can be embedded in R/sup 3/. Homology computation is a pure combinatorial problem of considerable intrinsic interest. While the worst-case bounds obtained for this algorithm are poor, it is argued that many triangulations (in general) and virtually all triangulations in design are very sparse in a particular sense. This sparseness measure is formalized, and a probabilistic analysis of the sparse case is performed to show that the expected running time, of the algorithm is roughly quadratic in the geometric complexity (number of simplices) and linear in the dimension.<>
{"title":"On the complexity of computing the homology type of a triangulation","authors":"B. Donald, Davied Renpan Chang","doi":"10.1109/SFCS.1991.185432","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185432","url":null,"abstract":"An algorithm for computing the homology type of a triangulation is analyzed. By triangulation is meant a finite simplicial complex; its homology type is given by its homology groups (with integer coefficients). The algorithm could be used in computer-aided design to tell whether two finite-element meshes or Bezier-spline surfaces are of the same topological type, and whether they can be embedded in R/sup 3/. Homology computation is a pure combinatorial problem of considerable intrinsic interest. While the worst-case bounds obtained for this algorithm are poor, it is argued that many triangulations (in general) and virtually all triangulations in design are very sparse in a particular sense. This sparseness measure is formalized, and a probabilistic analysis of the sparse case is performed to show that the expected running time, of the algorithm is roughly quadratic in the geometric complexity (number of simplices) and linear in the dimension.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"17 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":"127304985","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.1991.185429
G. Frederickson
Ambivalent data structures are presented for several problems on undirected graphs. They are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log beta (m,n)+min(k/sup 3/2/, km/sup 1/2/)) time, where m is the number of edges and n the number of vertices in the graph. The techniques are extended to find the k smallest spanning trees in an embedded planar graph in O(n+k(log n)/sup 3/) time. Ambivalent data structures are also used to maintain dynamically 2-edge-connectivity information. Edges and vertices can be inserted or deleted in O(m/sup 1/2/) time, and a query as to whether two vertices are in the same 2-edge-connected component can be answered in O(log n) time, where m and n are understood to be the current number of edges and vertices, respectively. Again, the techniques are extended to maintain an embedded planar graph so that edges and vertices can be inserted or deleted in O((log n)/sup 3/) time, and a query answered in O(log n) time.<>
{"title":"Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees","authors":"G. Frederickson","doi":"10.1109/SFCS.1991.185429","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185429","url":null,"abstract":"Ambivalent data structures are presented for several problems on undirected graphs. They are used in finding the k smallest spanning trees of a weighted undirected graph in O(m log beta (m,n)+min(k/sup 3/2/, km/sup 1/2/)) time, where m is the number of edges and n the number of vertices in the graph. The techniques are extended to find the k smallest spanning trees in an embedded planar graph in O(n+k(log n)/sup 3/) time. Ambivalent data structures are also used to maintain dynamically 2-edge-connectivity information. Edges and vertices can be inserted or deleted in O(m/sup 1/2/) time, and a query as to whether two vertices are in the same 2-edge-connected component can be answered in O(log n) time, where m and n are understood to be the current number of edges and vertices, respectively. Again, the techniques are extended to maintain an embedded planar graph so that edges and vertices can be inserted or deleted in O((log n)/sup 3/) time, and a query answered in O(log n) time.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"27 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":"125414237","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.1991.185445
A. Amir, Martín Farach-Colton
Semiadaptive and fully adaptive dictionary matching algorithms are presented. In the fully adaptive algorithm, the dictionary is processed in time O( mod D mod log mod D mod ). Inserting a new pattern P/sub k+1/ into the dictionary can be done in time O mod P/sub K+1/ mod log mod D mod ). A dictionary pattern can be deleted in time O(log mod D mod ). Text scanning is accomplished in time O( mod T mod log mod D mod ). Also presented is a parallel version of the algorithm with optimal speedup for the dictionary construction and pattern addition phase and a logarithmic overhead in the text scan phase. The method used incorporates a new way of using suffix trees as well as a new data structure in which the suffix tree is embedded for the sequential algorithm.<>
提出了半自适应和全自适应字典匹配算法。在全自适应算法中，字典的处理时间为O(mod D mod log mod D mod)。在字典中插入一个新的模式P/ k+1/可以在时间0 mod P/ k+1/ mod log mod D mod中完成。字典模式可以在时间O(log mod D mod)中删除。文本扫描在时间O(T mod log mod D mod)完成。本文还介绍了该算法的并行版本，该算法在字典构建和模式添加阶段具有最佳加速，而在文本扫描阶段具有对数开销。该方法采用了一种使用后缀树的新方法，以及一种新的数据结构，其中后缀树嵌入了顺序算法。
{"title":"Adaptive dictionary matching","authors":"A. Amir, Martín Farach-Colton","doi":"10.1109/SFCS.1991.185445","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185445","url":null,"abstract":"Semiadaptive and fully adaptive dictionary matching algorithms are presented. In the fully adaptive algorithm, the dictionary is processed in time O( mod D mod log mod D mod ). Inserting a new pattern P/sub k+1/ into the dictionary can be done in time O mod P/sub K+1/ mod log mod D mod ). A dictionary pattern can be deleted in time O(log mod D mod ). Text scanning is accomplished in time O( mod T mod log mod D mod ). Also presented is a parallel version of the algorithm with optimal speedup for the dictionary construction and pattern addition phase and a logarithmic overhead in the text scan phase. The method used incorporates a new way of using suffix trees as well as a new data structure in which the suffix tree is embedded for the sequential algorithm.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"49 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":"126625737","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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