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.ESA.2018.70
URN: urn:nbn:de:0030-drops-95339
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9533/
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Schmidt, Daniel R. ; Zey, Bernd ; Margot, François

An Exact Algorithm for the Steiner Forest Problem

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LIPIcs-ESA-2018-70.pdf (0.6 MB)

Abstract

The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem.

BibTeX - Entry

@InProceedings{schmidt_et_al:LIPIcs:2018:9533,
  author =	{Daniel R. Schmidt and Bernd Zey and Fran{\c{c}}ois Margot},
  title =	{{An Exact Algorithm for the Steiner Forest Problem}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9533},
  URN =		{urn:nbn:de:0030-drops-95339},
  doi =		{10.4230/LIPIcs.ESA.2018.70},
  annote =	{Keywords: branch-and-bound algorithms, Steiner network problems}
}

Keywords: branch-and-bound algorithms, Steiner network problems
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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