License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.54
URN: urn:nbn:de:0030-drops-115500
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11550/
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Eppstein, David ; Goodrich, Michael T. ; Liu, James A. ; Matias, Pedro

Tracking Paths in Planar Graphs

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LIPIcs-ISAAC-2019-54.pdf (0.7 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{eppstein_et_al:LIPIcs:2019:11550,
  author =	{David Eppstein and Michael T. Goodrich and James A. Liu and Pedro Matias},
  title =	{{Tracking Paths in Planar Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11550},
  URN =		{urn:nbn:de:0030-drops-115500},
  doi =		{10.4230/LIPIcs.ISAAC.2019.54},
  annote =	{Keywords: Approximation Algorithm, Courcelle's Theorem, Clique-Width, Planar, 3-SAT, Graph Algorithms, NP-Hardness}
}

Keywords: Approximation Algorithm, Courcelle's Theorem, Clique-Width, Planar, 3-SAT, Graph Algorithms, NP-Hardness
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019


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