## Finding the k Shortest Paths in Parallel (2000)

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### BibTeX

@MISC{Ruppert00findingthe,

author = {Eric Ruppert},

title = {Finding the k Shortest Paths in Parallel},

year = {2000}

}

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### 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 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 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. Key Words. Parallel graph algorithms, Data structures, Shortest paths. 1. Introduction. The problem of finding shortest paths in an edge-weighted graph is an important and well-studied problem in computer science. The more general problem of computing the k shortest paths between vertices of...