Finding the k Shortest Simple Paths: A New Algorithm and its Implementation

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Finding the k Shortest Simple Paths: A New Algorithm and its Implementation

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by John Hershberger , Matthew Maxel , Subhash Suri

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27 - 2 self

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@MISC{Hershberger_findingthe,
    author = {John Hershberger and Matthew Maxel and Subhash Suri},
    title = {Finding the k Shortest Simple Paths: A New Algorithm and its Implementation},
    year = {}
}

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Abstract

We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed recently by Hershberger and Suri [7], and can yield a factor #(n) improvement for this problem. But there is a caveat: the fast replacement paths subroutine is known to fail for some directed graphs. However, the failure is easily detected, and so our k shortest paths algorithm optimistically uses the fast subroutine, then switches to a slower but correct algorithm if a failure is detected. Thus the algorithm achieves its #(n) speed advantage only when the optimism is justified. Our empirical results show that the replacement paths failure is a rare phenomenon, and the new algorithm outperforms the current best algorithms; the improvement can be substantial in large graphs. For instance, on GIS map data with about 5000 nodes and 12000 edges, our algorithm is 4-8 times faster. In synthetic graphs modeling wireless ad hoc networks, our algorithm is about 20 times faster.

Keyphrases

new algorithm shortest simple path directed graph rare phenomenon replacement path speed advantage replacement path failure wireless ad hoc network fast subroutine large graph empirical result synthetic graph 4-8 time fast replacement path subroutine gi map data

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