eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
54:1
54:17
10.4230/LIPIcs.ISAAC.2019.54
article
Tracking Paths in Planar Graphs
Eppstein, David
1
Goodrich, Michael T.
1
https://orcid.org/0000-0002-8943-191X
Liu, James A.
1
Matias, Pedro
1
https://orcid.org/0000-0003-0664-9145
Department of Computer Science, University of California, Irvine, USA
We consider the NP-complete problem of tracking paths in a graph, first introduced by Banik et al. [Banik et al., 2017]. Given an undirected graph with a source s and a destination t, find the smallest subset of vertices whose intersection with any s-t 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.54/LIPIcs.ISAAC.2019.54.pdf
Approximation Algorithm
Courcelle’s Theorem
Clique-Width
Planar
3-SAT
Graph Algorithms
NP-Hardness