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Tracking Paths in Planar Graphs

By David Eppstein, Michael T. Goodrich, James A. Liu and Pedro Matias


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\u27s theorem, that it can be solved in linear time for graphs of bounded-clique width, when its clique decomposition is given in advance

Topics: Approximation Algorithm, Courcelle\u27s Theorem, Clique-Width, Planar, 3-SAT, Graph Algorithms, NP-Hardness, Data processing Computer science
Publisher: LIPIcs - Leibniz International Proceedings in Informatics. 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Year: 2019
DOI identifier: 10.4230/LIPIcs.ISAAC.2019.54
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