Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard

  • Authors:

  • Irène Charon;Olivier Hudry;Antoine Lobstein

  • Affiliations:

  • Département Informatique et Réseaux, Centre National de la Recherche Scientifique, URA 820, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris ...;Département Informatique et Réseaux, Centre National de la Recherche Scientifique, URA 820, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris ...;Département Informatique et Réseaux, Centre National de la Recherche Scientifique, URA 820, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

Let G = (V,E) be an undirected graph and C a subset of vertices. If the sets Br(υ) ∩ C, υ ∈ V (respectively, υ ∈ V\C), are all nonempty and different, where Br(υ) denotes the set of all points within distance r from υ, we call C an r-identifying code (respectively, an r-locating-dominating code). We prove that, given a graph G and an integer k, the decision problem of the existence of an r-identifying code, or of an r-locating-dominating code, of size at most k in G, is NP-complete for any r.