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.SWAT.2016.3
URN: urn:nbn:de:0030-drops-60323
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6032/
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Friggstad, Zachary ; Könemann, Jochen ; Shadravan, Mohammad

A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs

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LIPIcs-SWAT-2016-3.pdf (0.5 MB)

Abstract

We demonstrate that the integrality gap of the natural cut-based LP relaxation for the directed Steiner tree problem is O(log k) in quasi-bipartite graphs with k terminals. Such instances can be seen to generalize set cover, so the integrality gap analysis is tight up to a constant factor. A novel aspect of our approach is that we use the primal-dual method; a technique that is rarely used in designing approximation algorithms for network design problems in directed graphs.

BibTeX - Entry

@InProceedings{friggstad_et_al:LIPIcs:2016:6032,
  author =	{Zachary Friggstad and Jochen K{\"o}nemann and Mohammad Shadravan},
  title =	{{A Logarithmic Integrality Gap Bound for Directed Steiner Tree in Quasi-bipartite Graphs }},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6032},
  URN =		{urn:nbn:de:0030-drops-60323},
  doi =		{10.4230/LIPIcs.SWAT.2016.3},
  annote =	{Keywords: Approximation algorithm, Primal-Dual algorithm, Directed Steiner tree}
}

Keywords: Approximation algorithm, Primal-Dual algorithm, Directed Steiner tree
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

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