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

^∗Work partially supported by an Australian Research Council Grant and done during the author's visit at Abo Akademi University

Abstract

Let Gbe a connected, undirected and weighted graph with nvertices and medges. A most vital edge of Gwith 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 time using processors on a CRCW PRAM and time using processors on an EREW PRAM respectively. It significantly improves the known results of time and O(m) processors on the CRCW PRAM [10,13], and of time and processors on the CREW PRAM [13], and time using processors and time using processors on the EREW PRAM, respectivel.

Keywords:

• Edge replacement
• Minimum spanning tree
• Most vital edge
• Parallel algorithm
• PRAM

C.R. Categories:

• F.2.2
• G.2.2

^∗Work partially supported by an Australian Research Council Grant and done during the author's visit at Abo Akademi University

^† [email protected]

^∗Work partially supported by an Australian Research Council Grant and done during the author's visit at Abo Akademi University

^† [email protected]

Notes

^∗Work partially supported by an Australian Research Council Grant and done during the author's visit at Abo Akademi University

^† [email protected]