## Parallel Algorithms for the k Shortest Paths and Related Problems (1996)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Ruppert96parallelalgorithms,

author = {Eric Ruppert},

title = {Parallel Algorithms for the k Shortest Paths and Related Problems},

year = {1996}

}

### OpenURL

### Abstract

A parallel algorithm is developed to find the k shortest paths between pairs of vertices in an edge-weighted directed graph. The concurrent-read exclusive-write PRAM is used as the model of computation. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from each 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. Parallel algorithms are also described for a weighted version of the problem of selecting an element of given rank from an unsorted array and for the selection of the kth smallest element in a matrix with sorted columns. The k shortest paths algorithm is applied to obtain a parallel implementation of a dynamic programming algorithm for the list Viterbi decoding problem, where one must find the most probable state sequences of a Markov process, given noisy obser...