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Approximation Algorithms for Node-Weighted Prize-Collecting Steiner Tree Problems on Planar Graphs Byrka, Jaroslaw Lewandowski, Mateusz Moldenhauer, Carsten approximation algorithms Node-Weighted Steiner Tree primal-dual algorithm LMP planar graphs 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]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jaroslaw Byrka and Mateusz Lewandowski and Carsten Moldenhauer 2016 Is Part Of LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2016.2 urn:nbn:de:0030-drops-60313 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.2 eng https://creativecommons.org/licenses/by/3.0/legalcode