Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185370
J. Matoussek
The author considers the halfspace range reporting problem: Given a finite set P of points in E/sup d/, preprocess it so that given a query halfspace gamma , the points of p intersection gamma can be reported efficiently. It is shown that, with almost linear storage, this problem can be solved substantially more efficiently than the more general simplex range searching problem. A data structure for halfspace range reporting in dimensions d>or=4 is given. It uses O(n log log n) space and O (n log n) deterministic preprocessing time. The query time is also given. Results for the halfspace emptiness problem, where one only wants to know whether P intersection gamma is empty, are also presented.<>
{"title":"Reporting points in halfspaces","authors":"J. Matoussek","doi":"10.1109/SFCS.1991.185370","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185370","url":null,"abstract":"The author considers the halfspace range reporting problem: Given a finite set P of points in E/sup d/, preprocess it so that given a query halfspace gamma , the points of p intersection gamma can be reported efficiently. It is shown that, with almost linear storage, this problem can be solved substantially more efficiently than the more general simplex range searching problem. A data structure for halfspace range reporting in dimensions d>or=4 is given. It uses O(n log log n) space and O (n log n) deterministic preprocessing time. The query time is also given. Results for the halfspace emptiness problem, where one only wants to know whether P intersection gamma is empty, are also presented.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"47 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":"124923373","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.1991.185368
K. Mulmuley
A randomized technique, called dynamic shuffling, is given for multidimensional dynamic search. This technique, when specialized to the problem of searching in sorted lists, yields the previously known randomized binary trees (treaps). The crux of the technique is a multidimensional generalization of the rotation operation on binary search trees. Simultaneously, it is shown how to dynamize the randomized incremental algorithms so as to allow additions as well as deletions of objects. The techniques are based on remembering the history of the actual or imaginary sequence of updates. The techniques are applied to several problems in computational geometry.<>
{"title":"Randomized multidimensional search trees: lazy balancing and dynamic shuffling","authors":"K. Mulmuley","doi":"10.1109/SFCS.1991.185368","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185368","url":null,"abstract":"A randomized technique, called dynamic shuffling, is given for multidimensional dynamic search. This technique, when specialized to the problem of searching in sorted lists, yields the previously known randomized binary trees (treaps). The crux of the technique is a multidimensional generalization of the rotation operation on binary search trees. Simultaneously, it is shown how to dynamize the randomized incremental algorithms so as to allow additions as well as deletions of objects. The techniques are based on remembering the history of the actual or imaginary sequence of updates. The techniques are applied to several problems in computational geometry.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"40 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":"116036970","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.1991.185428
Amir M. Ben-Amram, Z. Galil
A technique is described for deriving lower bounds and tradeoffs for data structure problems. Two quantities are defined. The output variability depends only on the model of computation. It characterizes in some sense the power of a model. The problem variability depends only on the problem under consideration. It characterizes in some sense the difficulty of the problem. The first theorem states that if a model's output variability is smaller than the problem variability, a lower bound on the worst case (average case) time for the problem follows. A RAM that can add, subtract and compare unbounded integers is considered. The second theorem gives an upper bound on the output variability of this model. The two theorems are used to derive lower bounds for the union-find problem in this RAM.<>
{"title":"Lower bounds for data structure problems on RAMs","authors":"Amir M. Ben-Amram, Z. Galil","doi":"10.1109/SFCS.1991.185428","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185428","url":null,"abstract":"A technique is described for deriving lower bounds and tradeoffs for data structure problems. Two quantities are defined. The output variability depends only on the model of computation. It characterizes in some sense the power of a model. The problem variability depends only on the problem under consideration. It characterizes in some sense the difficulty of the problem. The first theorem states that if a model's output variability is smaller than the problem variability, a lower bound on the worst case (average case) time for the problem follows. A RAM that can add, subtract and compare unbounded integers is considered. The second theorem gives an upper bound on the output variability of this model. The two theorems are used to derive lower bounds for the union-find problem in this RAM.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"88 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":"132155598","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.1991.185453
H. Gabow
A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<>
{"title":"Applications of a poset representation to edge connectivity and graph rigidity","authors":"H. Gabow","doi":"10.1109/SFCS.1991.185453","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185453","url":null,"abstract":"A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"34 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":"127548788","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 : 1991-05-01DOI: 10.1109/SFCS.1991.185379
Weiguo Wang
Earlier work of P. Gacs and J. Reif (see J. Comput. Syst. Sci., vol.36, no.2, p.125-147 (1988)) on reliable computation using cellular automata is extended to asynchronous cellular automata. The goal is to find ways to implement computations of arbitrary size by a homogeneous asynchronous array of unreliable elementary components. An asynchronous two-dimensional cellular automaton is constructed so that given any computation and reliability requirement, a program can be found for such an automaton that performs the computation with probability that meets the reliability requirement. This is the strongest among the published results on reliable computation in an asynchronous environment. It is stronger than its asynchronous counterpart in the sense that it removes the assumption of a fault-free global synchronization clock underlying a synchronous system.<>
P. Gacs和J. Reif的早期工作(参见J. Comput。系统。科学。第36卷，没有。2, p.125-147(1988))关于使用元胞自动机进行可靠计算的研究扩展到异步元胞自动机。目标是找到通过不可靠基本组件的同构异步数组实现任意大小计算的方法。构造了一个异步二维元胞自动机，以便给定任何计算和可靠性要求，可以为这样的自动机找到一个程序，该程序以满足可靠性要求的概率执行计算。这是关于异步环境中可靠计算的已发布结果中最强的。它比其异步对应物更强，因为它消除了同步系统底层的无故障全局同步时钟的假设。
{"title":"An asynchronous two-dimensional self-correcting cellular automaton","authors":"Weiguo Wang","doi":"10.1109/SFCS.1991.185379","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185379","url":null,"abstract":"Earlier work of P. Gacs and J. Reif (see J. Comput. Syst. Sci., vol.36, no.2, p.125-147 (1988)) on reliable computation using cellular automata is extended to asynchronous cellular automata. The goal is to find ways to implement computations of arbitrary size by a homogeneous asynchronous array of unreliable elementary components. An asynchronous two-dimensional cellular automaton is constructed so that given any computation and reliability requirement, a program can be found for such an automaton that performs the computation with probability that meets the reliability requirement. This is the strongest among the published results on reliable computation in an asynchronous environment. It is stronger than its asynchronous counterpart in the sense that it removes the assumption of a fault-free global synchronization clock underlying a synchronous system.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124759882","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 : 1900-01-01DOI: 10.1109/SFCS.1991.185395
J. von zur Gathen
Optimal sequential and parallel algorithms for exponentiation in a finite field extension are presented, assuming that a normal basis over the ground field is given.<>
给出了有限域扩展中求幂的最优顺序和并行算法，其条件是给定了地面域上的正规基。
{"title":"Efficient exponentiation in finite field","authors":"J. von zur Gathen","doi":"10.1109/SFCS.1991.185395","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185395","url":null,"abstract":"Optimal sequential and parallel algorithms for exponentiation in a finite field extension are presented, assuming that a normal basis over the ground field is given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123507138","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 : 1900-01-01DOI: 10.1109/SFCS.1991.185434
J. Blomer
For a certain sum of radicals the author presents a Monte Carlo algorithm that runs in polynomial time to decide whether the sum is contained in some number field Q( alpha ), and, if so, its coefficient representation in Q( alpha ) is computed. As a special case the algorithm decides whether the sum is zero. The main algorithm is based on a subalgorithm which is of interest in its own right. This algorithm uses probabilistic methods to check for an element beta of an arbitrary (not necessarily) real algebraic number field Q( alpha ) and some positive rational integer r whether there exists an rth root of beta in Q( alpha ).<>
{"title":"Computing sums of radicals in polynomial time","authors":"J. Blomer","doi":"10.1109/SFCS.1991.185434","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185434","url":null,"abstract":"For a certain sum of radicals the author presents a Monte Carlo algorithm that runs in polynomial time to decide whether the sum is contained in some number field Q( alpha ), and, if so, its coefficient representation in Q( alpha ) is computed. As a special case the algorithm decides whether the sum is zero. The main algorithm is based on a subalgorithm which is of interest in its own right. This algorithm uses probabilistic methods to check for an element beta of an arbitrary (not necessarily) real algebraic number field Q( alpha ) and some positive rational integer r whether there exists an rth root of beta in Q( alpha ).<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126343320","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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