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DOI: 10.4230/LIPIcs.SWAT.2016.2
URN: urn:nbn:de:0030-drops-60313
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6031/
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Byrka, Jaroslaw ; Lewandowski, Mateusz ; Moldenhauer, Carsten

Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs

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LIPIcs-SWAT-2016-2.pdf (0.5 MB)


Abstract

We study the prize-collecting version of the node-weighted Steiner tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a 2.88-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with a threshold rounding technique and utilizing the 2.4-approximation of Berman and Yaroslavtsev [6] for the version without penalties. We also give a primal-dual 4-approximation algorithm for the more general forest version using techniques introduced by Hajiaghay and Jain [17].

BibTeX - Entry

@InProceedings{byrka_et_al:LIPIcs:2016:6031,
  author =	{Jaroslaw Byrka and Mateusz Lewandowski and Carsten Moldenhauer},
  title =	{{Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{2:1--2:14},
  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/2016/6031},
  URN =		{urn:nbn:de:0030-drops-60313},
  doi =		{10.4230/LIPIcs.SWAT.2016.2},
  annote =	{Keywords: approximation algorithms, Node-Weighted Steiner Tree, primal-dual algorithm, LMP, planar graphs}
}

Keywords: approximation algorithms, Node-Weighted Steiner Tree, primal-dual algorithm, LMP, planar graphs
Seminar: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 21.06.2016


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