NC Algorithms for the Single Most Vital Edge Problem with Respect to All Pairs Shortest Paths

For a weighted, undirected graph G = V;E where jVj = n and jEj = m, we examine the single most vital edge with respect to two measurements related to all-pairs shortest paths APSP. The rst measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of a tree edge. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in Ologn time using mn2 processors and Omn2 space on the MINIMUM CRCW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is de ned as the longest of these distances. The Most vital edge with respect to the diameter is the edge lying on such a u , v shortest path which when removed causes the greatest increase in the diameter. We show how to modify ...

• Type: Conference
• Year: 1998
• Where: IPPS
• Authors: Sven Venema, Hong Shen, Francis Suraweera
• Keywords: Distributed And Parallel Computing, IPPS 1998, Shortest Distance, Shortest Path, Vertex Pair