{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T07:13:00Z","timestamp":1696921980195},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2012,7,18]],"date-time":"2012-07-18T00:00:00Z","timestamp":1342569600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"ANR Project IDEA","award":["ANR-08-EMER-007"],"award-info":[{"award-number":["ANR-08-EMER-007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats: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\n<jats:styled-content>\\documentclass{article}\\usepackage{mathrsfs, amsmath, amssymb}\\pagestyle{empty}\\begin{document} $\\mathbb{Z}^2$ \\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>\nwhere one sensor can check its neighbors within Euclidean distance <jats:italic>r<\/jats: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 <jats:italic>r<\/jats:italic>. We also provide infinite families of values <jats:italic>r<\/jats:italic> with optimal such codes and study the case of small values of <jats:italic>r<\/jats:italic>. \u00a9 2012 Wiley Periodicals, Inc. 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Available athttp:\/\/perso.enst.fr\/\u223clobstein\/debutBIBidetlocdom.pdf. 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