An O(log N) Time Common CRCW PRAM Algorithm for Minimum Spanning Tree

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(lognlog*n) time with (m+n) processors and expected O(logn) time with (m+n) logn processors. This represents a significant improvement in terms of efficiency over the previous best results for solving this problem ona Common CRCW PRAM and compares favourably 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 [2]. 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.