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, Paris Cedex, France;CNRS, Laboratoire Leibniz, Grenoble Cedex, France;GET, Télécom Paris & CNRS, Paris Cedex, France;CNRS, GET, Télécom Paris, Paris Cedex, France;CNRS, Laboratoire Leibniz, Grenoble Cedex, France;CNRS, Laboratoire Leibniz, 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 Br- (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 Br- (v)∩C are all nonempty and different, then we call C an r-identifying code. We describe a linear algorithm which gives a minimum I-identifying code in any oriented tree.