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DOI: 10.4230/LIPIcs.SWAT.2016.2
Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs

Authors: Jaroslaw Byrka, Mateusz Lewandowski, and Carsten Moldenhauer

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

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].
Cite as

Jaroslaw Byrka, Mateusz Lewandowski, and Carsten Moldenhauer. Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{byrka_et_al:LIPIcs.SWAT.2016.2,
  author =	{Byrka, Jaroslaw and Lewandowski, Mateusz and Moldenhauer, Carsten},
  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 =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.2},
  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}
}
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