O(Kn2) ALGORITHM FOR K SHORTEST SIMPLE PATHS IN AN UNDIRECTED GRAPH WITH NONNEGATIVE ARC LENGTH.

An O(Kn)**2 algorithm to find K shortest simple paths in an undirected graph with nonnegative arc length is presented. Here n is the number of vertices in a graph. First a shortest simple path is obtained by the Dijkstra method. The second through kth shortest simple paths are then successively obtained by systematically partitioning the set of paths to avoid duplication. The partitioning is accomplished by repeatedly calling a subroutine to find in O(n**2) time the shortest simple paths not containing a given initial subpath of the first shortest simple path.