2000
DOI: 10.1137/s0895480199360990
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Abstract: In an undirected graph G = (V; E) a subset C V is called an identifying code, if the sets B1 (v) \ C consisting of all elements of C within distance one from the vertex v are nonempty and di erent. We take G to be the in nite hexagonal grid, and show that the density of any identifying code is at least 16=39 and that there is an identifying code of density 3=7.

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Cited by 44 publications
(37 citation statements)
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“…Since at every iteration, we add one or more codewords and do not remove any codeword, the set of codewords in C and in every component of C forms an 5 identifying code. Hence, Lemmas 5.1 and 5.2 invariably hold after every iteration.…”
Section: Performance Analysismentioning
confidence: 99%
See 1 more Smart Citation
“…Since at every iteration, we add one or more codewords and do not remove any codeword, the set of codewords in C and in every component of C forms an 5 identifying code. Hence, Lemmas 5.1 and 5.2 invariably hold after every iteration.…”
Section: Performance Analysismentioning
confidence: 99%
“…Although introduced only twelve years ago [1], identifying codes have been linked to a number of deeply researched theoretical foundations, including super-imposed codes [2], covering codes [1,3], locating-dominating sets [4], and tilings [5][6][7][8]. They have also been generalized and used for detecting faults or failures in multi-processor systems [1], RF-based localization in harsh environments [9][10][11], and routing in networks [12].…”
Section: Introductionmentioning
confidence: 99%
“…Particular interest was dedicated to grids as many processor networks have a grid topology. Many results have been obtained on square grids [4,1,9,2,11], triangular grids [12,10], and hexagonal grids [5,7,8]. In this paper, we study king grids, which are strong products of two paths.…”
Section: Introductionmentioning
confidence: 99%
“…Significant efforts in the research of identifying codes and their variants have focused on finding efficient constructions in two dimensional lattices, grids and Hamming spaces (see [12,[23][24][25][26], and [6] for a summary of recent results). Until recently, little has been published towards a polynomial time approximation algorithm for arbitrary graphs.…”
Section: Introductionmentioning
confidence: 99%