Tracking Paths in Planar Graphs
Discrete Mathematics
2019-10-01 v2 Data Structures and Algorithms
Abstract
We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et. al. [3]. Given an undirected graph with a source and a destination , find the smallest subset of vertices whose intersection with any path results in a unique sequence. In this paper, we show that this problem remains NP-complete when the graph is planar and we give a 4-approximation algorithm in this setting. We also show, via Courcelle's theorem, that it can be solved in linear time for graphs of bounded-clique width, when its clique decomposition is given in advance.
Cite
@article{arxiv.1908.05445,
title = {Tracking Paths in Planar Graphs},
author = {David Eppstein and Michael T. Goodrich and James A. Liu and Pedro Matias},
journal= {arXiv preprint arXiv:1908.05445},
year = {2019}
}