License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2016.49
URN: urn:nbn:de:0030-drops-68199
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6819/
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Kurz, Denis ; Mutzel, Petra

A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

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LIPIcs-ISAAC-2016-49.pdf (0.5 MB)

Abstract

We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein’s algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm [Networks, 1971] and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n+m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude.

BibTeX - Entry

@InProceedings{kurz_et_al:LIPIcs:2016:6819,
  author =	{Denis Kurz and Petra Mutzel},
  title =	{{A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{49:1--49:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Seok-Hee Hong},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6819},
  URN =		{urn:nbn:de:0030-drops-68199},
  doi =		{10.4230/LIPIcs.ISAAC.2016.49},
  annote =	{Keywords: directed graph, k-best, shortest path, simple path, weighted graph}
}

Keywords: directed graph, k-best, shortest path, simple path, weighted graph
Collection: 27th International Symposium on Algorithms and Computation (ISAAC 2016)
Issue Date: 2016
Date of publication: 07.12.2016

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