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Tracking Routes in Communication Networks

  • Davide Bilò
  • Luciano Gualà
  • Stefano LeucciEmail author
  • Guido Proietti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)

Abstract

The minimum tracking set problem is an optimization problem that deals with monitoring communication paths that can be used for exchanging point-to-point messages using as few tracking devices as possible. More precisely, a tracking set of a given graph G and a set of source-destination pairs of vertices, is a subset T of vertices of G such that the vertices in T traversed by any source-destination shortest path P uniquely identify P. The minimum tracking set problem has been introduced in [Banik et al., CIAC 2017] for the case of a single source-destination pair. There, the authors show that the problem is APX-hard and that it can be 2-approximated for the class of planar graphs, even though no hardness result is known for this case. In this paper we focus on the case of multiple source-destination pairs and we present the first \(\widetilde{O}(\sqrt{n})\)-approximation algorithm for general graphs. Moreover, we prove that the problem remains NP-hard even for cubic planar graphs and all pairs \(S \times D\), where S and D are the sets of sources and destinations, respectively. Finally, for the case of a single source-destination pair, we design an (exact) FPT algorithm w.r.t. the maximum number of vertices at the same distance from the source.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Humanities and Social SciencesUniversity of SassariSassariItaly
  2. 2.Department of Enterprise EngineeringUniversity of Rome “Tor Vergata”RomeItaly
  3. 3.Department of Algorithms and ComplexityMax Planck Institut für InformatikSaarbrückenGermany
  4. 4.Department of Information Engineering, Computer Science and MathematicsUniversity of L’AquilaL’AquilaItaly
  5. 5.Institute for System Analysis and Computer Science “Antonio Ruberti” (IASI CNR)RomeItaly

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