Abstract.
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, using O(m+nk log2 k) work and O( log^3k log ^*k+ log n( log log k+ 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 in O( log k + log n) time, and O(n log n +L) work, where L is the total length of the output.
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Received July 2, 1997; revised June 18, 1998.
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Ruppert, E. Finding the k Shortest Paths in Parallel . Algorithmica 28, 242–254 (2000). https://doi.org/10.1007/s004530010038
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DOI: https://doi.org/10.1007/s004530010038