Identifying codes in some subgraphs of the square lattice

Authors:
Marc Daniel;Sylvain Gravier;Julien Moncel
Affiliations:
CNRS-UJF, ERTé "Maths à Modeler", Groupe de Recherche GéoD, Laboratoire Leibniz, 46 Avenue Félix Viallet, Grenoble Cedex F-38031, France;CNRS-UJF, ERTé "Maths à Modeler", Groupe de Recherche GéoD, Laboratoire Leibniz, 46 Avenue Félix Viallet, Grenoble Cedex F-38031, France;CNRS-UJF, ERTé "Maths à Modeler", Groupe de Recherche GéoD, Laboratoire Leibniz, 46 Avenue Félix Viallet, Grenoble Cedex F-38031, France
Venue:
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Year:
2004

Citing 4
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Abstract

An identifying code of a graph is a subset of vertices C such that the sets B(v) ∩ C are all nonempty and different. In this paper, we investigate the problem of finding identifying codes of minimum cardinality in strips and finite grids. We first give exact values for the strips of height 1 and 2, then we give general bounds for strips and finite grids. Finally, we give a sublinear algorithm which finds the minimum cardinality of an identifying code in a restricted class of graphs which includes the grid.