Showing papers by "Richard Cole published in 1986"
01 Nov 1986
TL;DR: A new deterministic coin tossing technique that provides for a fast and eff ient b reak ing of a symmetr ic s i tuat ion in paral le l is introduced.
Abstract: Several results concern ing para l le l a lgor i thms are improved. A part ial list of the new results includes: For r ank ing a l inked list of length n, O(lognlog~n) t ime using an op t ima l number of processors . For se lect ing the m-th smal les t out of n e lements O(lognlog'n) t ime using an op t imal number of processors. For g raph connect ivi ty O(lognlogt-~nlogt3~n) t ime using (m + n ) a (m ,n ) / ( l ogn logf2~n logt3~n) processors , and for f inding m in imum spanning forest in a g raph O(lognlogt-~nlogtS~n) t ime using (m+n)/(lognlog~2~n) processors , where n is the number of ver t ices and m is the number of edges. All the new algor i thms are de terminis t ic . These results provide an op t imal de terminis t ic paral le l a lgor i thm for list ranking that achieves poly-log t ime. Also , they prov ide an op t imal a lgor i thm for connect ivi ty which runs in a lmos t logar i thmic t ime when m>-nlog*n. This op t ima l a lgor i thm achieves logar i thmic t ime w h e n m = n t-~, where 0 < e _ < l . Our results are also s t rong enough to refute a known conjecture regard ing a l imit on the poss ible per formance of any paral le l a lgor i thm for the list rank ing p rob lem. This paper introduces a new deterministic coin tossing technique that provides for a fast and eff ic ient b reak ing of a symmetr ic s i tuat ion in paral le l . Prev ious ly , it was known how to break such symmet r i e s only by means of r andomiza t ion . Interestingly, the s t ructure of all the a lgor i thms in this paper fol low a pa rad igm which we call accelerating cascades. Given severa l a l te rna t ive para l le l a lgor i thms for the same prob lem, this paradigm constructs a new algor i thm for the same problem ou t of these a lgor i thms; the per formance of the new a lgor i thm compares favourab ly wi th that of any of its bui ld ing blocks.
203 citations
27 Oct 1986
TL;DR: A novel scheduling problem is defined; it is solved by repeated, rapid, approximate reschedulings, which leads to a first optimal PRAM algorithm for list ranking, which runs in logarithmic time.
Abstract: We study two parallel scheduling problems and their use in designing parallel algorithms. First, we define a novel scheduling problem; it is solved by repeated, rapid, approximate reschedulings. This leads to a first optimal PRAM algorithm for list ranking, which runs in logarithmic time. Our second scheduling result is for computing prefix sums of logn bit numbers. We give an optimal parallel algorithm for the problem which runs in sublogarithmic time. These two scheduling results together lead to logarithmic time PRAM algorithms for the connectivity, biconnectivity and minimum spanning tree problems. The connectivity and biconnectivity algorithms are optimal unless m = o(nlog*n), in graphs of n vertices and m edges.
196 citations
TL;DR: In this article, the worst-case space-time complexity of a large class of geometric retrieval problems has been shown to be O(n2 + e/log n, log n log(1/e) for arbitrary small e.
Abstract: A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n), g(n)) if the space requirement for D(X) is O(f) and the “locate run-time” required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n2 + e/log n, log n log(1/e)) space-time algorithm for the polygon retrieval problem, for arbitrarily small e, improving on the previous solution having complexity O(n7, log n).
59 citations
TL;DR: This paper investigates the circular retrieval problem and the k-nearest neighbor problem, for sets of n points in the Euclidean plane, and finds two similar data structures each solve both problems.
Abstract: This paper investigates the circular retrieval problem and the k-nearest neighbor problem, for sets of n points in the Euclidean plane. Two similar data structures each solve both problems. A deterministic structure uses space O(n(log n log log n)2), and a probabilistic structure uses space O(n log2 n). For both problems, these two structures answer a query that returns k points in O(k + log n) time.
45 citations
27 Oct 1986
TL;DR: An efficient algorithms for preprocessing of a 2-D polyhedral terrain so as to support fast ray shooting queries from a fixed point and for determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations are presented.
Abstract: We present efficient algorithms for the following geometric problems: (i) Preprocessing of a 2-D polyhedral terrain so as to support fast ray shooting queries from a fixed point. (ii) Determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations. (iii) Determining whether a given convex polygon can be translated and rotated so as to fit into another given polygonal region. (iv) Motion planning for a convex polygon in the plane amidst polygonal barriers. All our algorithms make use of Davenport Schinzel sequences and on some generalizations of them; these sequences are a powerful combinatorial tool applicable in contexts which involve the calculation of the pointwise maximum or minimum of a collection of functions.
30 citations