We present a probabilistic algorithm for finding the minimum spanning tree of a graph with n vertices and m edges on a Common CRWC PRAM. It uses expected O(log n log* n) time with (m + n) processors and expected O(log n) time with (m + n) log n processors. This represents a significant improvement in terms of efficiency over the previous best results for solving this problem on a Common CRCW PRAM and compares favorably with the best result for the Priority CRCW PRAM, a more powerful model. The algorithm presents a novel application of recent results on recursive *-tree data structures. An important contribution of this paper is (i) a strategy to schedule the growth of components in algorithms based on repeated graph-contractions and (ii) an amortized analysis technique to account for the scheduling overhead.
An O(log n) Time Common CRCW PRAM Algorithm for Minimum Spanning Tree
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