An O(logn) 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 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 [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.