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DOI: 10.4230/LIPIcs.SEA.2020.18
Space and Time Trade-Off for the k Shortest Simple Paths Problem

Authors: Ali Al Zoobi, David Coudert, and Nicolas Nisse

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
The k shortest simple path problem (kSSP) asks to compute a set of top-k shortest simple paths from a vertex s to a vertex t in a digraph. Yen (1971) proposed the first algorithm with the best known theoretical complexity of O(kn(m+n log n)) for a digraph with n vertices and m arcs. Since then, the problem has been widely studied from an algorithm engineering perspective, and impressive improvements have been achieved. In particular, Kurz and Mutzel (2016) proposed a sidetracks-based (SB) algorithm which is currently the fastest solution. In this work, we propose two improvements of this algorithm. We first show how to speed up the SB algorithm using dynamic updates of shortest path trees. We did experiments on some road networks of the 9th DIMAC'S challenge with up to about half a million nodes and one million arcs. Our computational results show an average speed up by a factor of 1.5 to 2 with a similar working memory consumption as SB. We then propose a second algorithm enabling to significantly reduce the working memory at the cost of an increase of the running time (up to two times slower). Our experiments on the same data set show, on average, a reduction by a factor of 1.5 to 2 of the working memory.
Cite as

Ali Al Zoobi, David Coudert, and Nicolas Nisse. Space and Time Trade-Off for the k Shortest Simple Paths Problem. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{alzoobi_et_al:LIPIcs.SEA.2020.18,
  author =	{Al Zoobi, Ali and Coudert, David and Nisse, Nicolas},
  title =	{{Space and Time Trade-Off for the k Shortest Simple Paths Problem}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.18},
  URN =		{urn:nbn:de:0030-drops-120925},
  doi =		{10.4230/LIPIcs.SEA.2020.18},
  annote =	{Keywords: k shortest simple paths, graph algorithm, space-time trade-off}
}
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