Identification in Z(2) using Euclidean balls

: Junnila V, Laihonen T

Publisher: ELSEVIER SCIENCE BV

: 2011

: Discrete Applied Mathematics

: DISCRETE APPLIED MATHEMATICS

: DISCRETE APPL MATH

: 5

: 159

: 5

: 335

: 343

: 9

: 0166-218X

DOI: https://doi.org/10.1016/j.dam.2010.12.008

: https://research.utu.fi/converis/portal/Publication/2324036

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 epsilon(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 epsilon(root 5) and epsilon(root 13). (C) 2010 Elsevier B.V. All rights reserved.

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