Improved parallel algorithms for finding the most vital edge of a graph with respect to minimum spanning tree

Let G be a connected, undirected and weighted graph with n vertices and nr edges. A most vital edge of G with respect to minimum spanning tree is an edge whose removal from G results in the greatest weight-increase in the minimum spanning tree of the remaining graph. This paper presents a fast parallel algorithm that computes the most vital edge of G in O(logn) time using O(max{n, m log log log n/log n}) processors on a CRCW PRAM and O(log nlog log n) time using O(max{m, n(2)/(log n log log n)}) processors on an EREW PRAM respectively. It significantly improves the known results of O(logn) time and O(m) processors on the CRCW PRAM [10, 13], and of O(log(2)n) time and O(n(2)/log(2)n) processors on the CREW PRAM [13], and O(n(l+epsilon)) time using nl-E processors and O(mlog(m/N)/N + n alpha(m, n)log(m/n)) time using N less than or equal to m log m/(n alpha(m, n)log(m/n)) processors on the EREW PRAM, respectively.