Tolerant identification with Euclidean balls. Issue 3 (18th July 2012)

• Record Type: Journal Article
• Authors: Junnila, Ville; Laihonen, Tero; Parreau, Aline
• Is Part Of: Networks. Volume 61:Issue 3(2013:May)
• Page Start: 212
• Page End: 225
• Publication Date: 2012-07-18
• Subjects: Network analysis (Planning) -- Periodicals; 658.4032
• DOI: 10.1002/net.21472
• Languages: English
• ISSNs: 0028-3045

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 article, we consider as sensors the set <tex-math notation="LaTeX"><![CDATA[\documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document} $\mathbb{Z}^2$ \end{document}]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg1x6qr1wz" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> where one sensor can check its neighbors within Euclidean distance <italic>r</italic>. We construct tolerant identifying codes in this network that are robust against some changes in the neighborhood monitored by each sensor. We give bounds for the smallest density of a tolerant identifying code for general values of <italic>r</italic>. We also provide infinite families of values <italic>r</italic> with optimal such codes and study the case of small values of <italic>r</italic>. © 2012 Wiley Periodicals, Inc. NETWORKS, 2013</p> </abstract>