Showing papers by "Uzi Vishkin published in 1985"
21 Oct 1985
TL;DR: An algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches (superfluous characters in either the text or the pattern are not allowed), which runs in O(k(m logm + n)) time.
Abstract: Consider the string matching problem where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern or a superfluous character in the text or a superfluous character in the pattern. Given a text of length n, a pattern of length m and an integer k, we present an algorithm for finding all occurrences of the pattern in the text, each with at most k differences. The algorithm runs in O(m2 + k2n) time. Given the same input we also present an algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches (superfluous characters in either the text or the pattern are not allowed). This algorithm runs in O(k(m logm + n)) time.
78 citations
TL;DR: La famille de modeles de calcul utilisee dans cet article est la famille des machines a acces aleatoire parallele (PRAM).
65 citations
TL;DR: The technique is extended to prove mT3 = Ω(n) trade-off for a class of "simpler" functions (includind Boolean Or) on a weaker model that forbids simultaneous write access, which improves the lower bound of Cook and Dwork when communication is limited.
Abstract: A new technique for proving lower bounds for parallel computation is introduced. This technique enables us to obtain, for the first time, nontrivial tight lower bounds for shared-memory models of parallel computation that allow several processors to have simultaneous access to the same memory location. Specifically, we use a concurrent-read concurrent-write model of parallel computation. It has p processors, each has access to a common memory of size m (also called communication width or width in short). The input to the problem is located in an additional read-only portion of the common memory.For a wide variety of problems (including parity, majority and summation) we show that the time complexity T (depth) and the communication width m are related by the trade-off curve $mT^2 = \Omega (n)$, (where n is the size of the input), regardless of the number of processors. Moreover, for every point on this curve with $m = O(n/\log ^2 n)$ we give a matching upper bound with the optimal number of processors.We e...
54 citations
15 Jul 1985
TL;DR: Given a text of length n and a pattern, this work presents a parallel linear algorithm for finding all occurrences of the pattern in the text in O(n/p) time using any number of p ≤ n/log n processors on a concurrent-read concurrent-write parallel random-access-machine.
Abstract: Given a text of length n and a pattern, we present a parallel linear algorithm for finding all occurrences of the pattern in the text. The algorithm runs in O(n/p) time using any number of p ≤ n/log n processors on a concurrent-read concurrent-write parallel random-access-machine.
36 citations
Proceedings Article•
15 Jul 1985
34 citations
TL;DR: An algorithm which finds a minimum vertex cover in a graph G(V, E) in time O (|V|+( a k )2 k 3 ) , where for connected graphs G the parameter a is defined as the minimum number of edges that must be added to a tree to produce G.
20 citations