# Finding the *k* shortest paths in parallel

Parallel Algorithms

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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 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.

## Topics

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