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Showing papers by "Richard Cole published in 1996"


Proceedings ArticleDOI
24 Jun 1996
TL;DR: A randomized c’RC\Y PRALI algorithm that finds a minimum spanning forest of an n-vertex graph in O(log n ) time and linear work is described, which shaves a factor of off the best previous running time for a linear-work algorithm.
Abstract: using random sampling Richard Cole” Philip N. Kleint Robert E. Tarjan$ New }“ork ITniversity Brown Unil-ersity Princeton [University aIId ~~~ Researcl~ Institute Jve describe a randomized c’RC\Y PRALI algorithm that finds a minimum spanning forest of an n-vertex graph in O(log n ) time and linear work. This shaves a factor of ?ioK* “ off the best previous running time for a linear-work algorithm. The novelty in our approach is to divide the conlpntatiou into two phases, the first of which finds only a partial solution. This idea has been used prevlonsly in parallel connected components algorithms.

63 citations


Proceedings ArticleDOI
28 Jan 1996
TL;DR: In this article, the authors considered the case when the trees are binary and gave an O(n log n) time algorithm for this problem, where n is the number of nodes in the tree.
Abstract: The Maximum Agreement Subtree problem is the following: Given two trees whose leaves are drawn from the same set of items (e.g., species), find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic. We consider the case which occurs frequently in practice, i.e., the case when the trees are binary, and give an O(n log n) time algorithm for this problem.

33 citations


Proceedings ArticleDOI
24 Jun 1996
TL;DR: It is shown that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in O((L+ D) C(D log D) B B) flit steps, which implies that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor.
Abstract: This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in O((L+ D) C(D log D) B B) flit steps, where a flit step is the time taken to transmit B flits, i.e., one flit per virtual channel, across a physical channel. We also prove a nearly matching lower bound; i.e., for any values of C, D, B, and L, where C, D B+1 and L=(1+0(1)) D, we show how to construct a network and a set of L-flit messages whose paths have congestion C and dilation D that require 0(LCD B B) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor significantly larger than B. We also present a simple randomized wormhole routing algorithm for the butterfly network. The algorithm routes any q-relation on the inputs and outputs doi:10.1006 jcss.2000.1701, available online at http: www.idealibrary.com on

21 citations


Journal ArticleDOI
TL;DR: This work describes ann-processor,O(log(n) log log log(n))-time CRCW algorithm to construct the Voronoi diagram for a set of point-sites in the plane.
Abstract: We describe ann-processor,O(log(n) log log(n))-time CRCW algorithm to construct the Voronoi diagram for a set ofn point-sites in the plane.

16 citations