Identification in Z(2) using Euclidean balls

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 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.