A Simple Algorithm For Replacement Paths Problem

Abstract

Let G=(V,E) (|V|=n and |E|=m) be an undirected graph with positive edge weights. Let PG(s,t) be a shortest s−t path in G. Let l be the number of edges in PG(s,t). The Edge Replacement Path problem is to compute a shortest s−t path in G\{e}, for every edge e in PG(s,t). The Node Replacement Path problem is to compute a shortest s−t path in G\{v}, for every vertex v in PG(s,t). In this paper we present an O(TSPT(G)+m+l2) time and O(m+l2) space algorithm for both the problems. Where, TSPT(G) is the asymptotic time to compute a single source shortest path tree in G. The proposed algorithm is simple and easy to implement.