A Simple Algorithm For Replacement Paths Problem

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+l ) time andO(m+l) 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.