Tolerant identification with Euclidean balls

TL;DR

This paper develops tolerant identifying codes in Euclidean grid networks, providing bounds and constructions that are robust against neighborhood changes, with applications to sensor networks.

Contribution

It introduces new bounds and constructions for tolerant identifying codes in Euclidean grids, expanding the understanding of robustness in sensor network identification.

Findings

Bounds for the smallest density of tolerant identifying codes.

Infinite families of optimal codes for certain parameters.

Analysis of small radius cases.

Abstract

The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. The identifying codes can be applied, for example, to sensor networks. In this paper, we consider as sensors the set Z^2 where one sensor can check its neighbours within Euclidean distance r. We construct tolerant identifying codes in this network that are robust against some changes in the neighbourhood monitored by each sensor. We give bounds for the smallest density of a tolerant identifying code for general values of r and Delta. We also provide infinite families of values (r,Delta) with optimal such codes and study the case of small values of r.