Showing papers by "Richard Cole published in 1991"
TL;DR: A new logarithmic time parallel (PRAM) algorithm for computing the connected components of undirected graphs which uses a novel technique for approximate parallel scheduling and implies logarathmic time optimal parallel algorithms for a number of other graph problems, including biconnectivity, Euler tours, strong orientation and st-numbering.
Abstract: Part I of this paper presented a novel technique for approximate parallel scheduling and a new logarithmic time optimal parallel algorithm for the list ranking problem. In this part, we give a new logarithmic time parallel (PRAM) algorithm for computing the connected components of undirected graphs which uses this scheduling technique. The connectivity algorithm is optimal unless m = o(n log∗ n) in graphs of n vertices and m edges. (log(k) denotes the kth iterate of the log function and log∗ n denotes the least i such that log(i) n ≤ 2). Using known results, this new algorithm implies logarithmic time optimal parallel algorithms for a number of other graph problems, including biconnectivity, Euler tours, strong orientation and st-numbering. Another contribution of the present paper is a parallel union/find algorithm.
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