English

Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs

Data Structures and Algorithms 2016-01-12 v1

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+ϵ2.88 + \epsilon)-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 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.

Keywords

Cite

@article{arxiv.1601.02481,
  title  = {Approximation algorithms for node-weighted prize-collecting Steiner tree problems on planar graphs},
  author = {Jarosław Byrka and Mateusz Lewandowski and Carsten Moldenhauer},
  journal= {arXiv preprint arXiv:1601.02481},
  year   = {2016}
}
R2 v1 2026-06-22T12:26:52.571Z