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 ()-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.
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}
}