A concurrent-read exclusive-write PRAM algorithm is developed to find 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 in O(m+nklog2k) work and O(log3klog*k+logn(loglogk+log*n)) time, assuming that a shortest path tree rooted at the destination is pre-computed. The paths themselves can be extracted from the implicit representation. Applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons are described.

Topics
Optimization algorithms, Graph theory
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