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Tracking Paths in Planar Graphs

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

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LIPIcs.ISAAC.2019.54.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Theory of computation → Computational complexity and cryptography
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Approximation Algorithm
  • Courcelle’s Theorem
  • Clique-Width
  • Planar
  • 3-SAT
  • Graph Algorithms
  • NP-Hardness

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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.

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David Eppstein, Michael T. Goodrich, James A. Liu, and Pedro Matias. Tracking Paths in Planar Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.54

Author Details

David Eppstein
  • Department of Computer Science, University of California, Irvine, USA
Michael T. Goodrich
  • Department of Computer Science, University of California, Irvine, USA
James A. Liu
  • Department of Computer Science, University of California, Irvine, USA
Pedro Matias
  • Department of Computer Science, University of California, Irvine, USA

Acknowledgements

We thank Nil Mamano for suggesting the problem of tracking paths on a graph.

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