Identification in Z2 using Euclidean balls

Authors:
Ville Junnila;Tero Laihonen
Affiliations:
Turku Centre for Computer Science TUCS, Finland and Department of Mathematics, University of Turku, FI-20014 Turku, Finland;Department of Mathematics, University of Turku, FI-20014 Turku, Finland
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 10
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Abstract

The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin. These codes find their application, for example, in sensor networks. The network is modelled by a graph. In this paper, the goal is to find good identifying codes in a natural setting, that is, in a graph E"r=(V,E) where V=Z^2 is the set of vertices and each vertex (sensor) can check its neighbours within Euclidean distance r. We also consider a graph closely connected to a well-studied king grid, which provides optimal identifying codes for E"5 and E"1"3.