Finding the k Shortest Paths in

A concurrent-read exclusive-write PRAM algorithm is developed to nd the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and m edges, using O(m + nk log 2 k) work and O(log 3 k log k + log n(log log k + log n)) time, assuming that a shortest path tree rooted at the destination is precomputed. The paths themselves can be extracted from the implicit representation in O(log k+log n) time, and O(n log n + L) work, where L is the total length of the output.