The longest detour problem on a shortest path tree

Abstract

In a biconnected graph, a detour from a vertex u to some destination vertex s when the edge(u,v) is not available in a shortest path<u,v,....,s>,The longest detour(LD)problem is to find an edge(u,v),called the detour-critical edge, along a shortest path<r,...,u,v,...,s>,such that the removal of (u,v) may cause maximum increment of vertices and edges, respectively, in a graph , in this paper, we are concerned with the LD problem with respect to a shortest path tree of a graph,An O(m a(m,n)) time algorithm for finding a detour-critical edge in a shortest path tree is presented in this paper, where a is a functional inverse of ackermann's function