A linear algorithm for minimum 1-identifying codes in oriented trees

  • Authors:
  • Irène Charon;Sylvain Gravier;Olivier Hudry;Antoine Lobstein;Michel Mollard;Julien Moncel

  • Affiliations:
  • GET, Télécom Paris & CNRS, LTCI UMR 5141, 46 rue Barrault 75634, Paris Cedex 13, France;CNRS, Laboratoire Leibniz, 46 avenue Félix Viallet 38031, Grenoble Cedex, France;GET, Télécom Paris & CNRS, LTCI UMR 5141, 46 rue Barrault 75634, Paris Cedex 13, France;CNRS, LTCI UMR 5141 & GET, Téélécom Paris, 46 rue Barrault 75634, Paris Cedex 13, France;CNRS, Laboratoire Leibniz, 46 avenue Félix Viallet 38031, Grenoble Cedex, France;CNRS, Laboratoire Leibniz, 46 avenue Félix Viallet 38031, Grenoble Cedex, France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2006

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Abstract

Consider an oriented graph G=(V,A), a subset of vertices C@?V, and an integer r=1; for any vertex v@?V, let B"r^-(v) denote the set of all vertices x such that there exists a path from x to v with at most r arcs. If for all vertices v@?V, the sets B"r^-(v)@?C are all nonempty and different, then we call C an r-identifying code. We describe a linear algorithm which gives a minimum 1-identifying code in any oriented tree.