A1 Refereed original research article in a scientific journal
On identifying codes in the hexagonal mesh
Authors: Honkala I, Laihonen T
Publisher: ELSEVIER SCIENCE BV
Publication year: 2004
Journal: Information Processing Letters
Journal name in source: INFORMATION PROCESSING LETTERS
Journal acronym: INFORM PROCESS LETT
Volume: 89
Issue: 1
First page : 9
Last page: 14
Number of pages: 6
ISSN: 0020-0190
DOI: https://doi.org/10.1016/j.ipl.2003.09.009(external)
Abstract
It is shown that, if r greater than or equal to 2, there exists an (r, less than or equal to 2)-identifying code in the infinite hexagonal mesh with density (5r + 2)/((r + 2)(2r + 1)) for even r and (5r + 1)/((dr + 1)(2r + 1)) for odd r. The optimal density of a (1, less than or equal to 2)-identifying code in the infinite hexagonal mesh is shown to be 2/3 and the optimal densities of (1, less than or equal to 3)- and (2, less than or equal to 3)-identifying codes are shown to be 1. (C) 2003 Elsevier B.V. All rights reserved.
It is shown that, if r greater than or equal to 2, there exists an (r, less than or equal to 2)-identifying code in the infinite hexagonal mesh with density (5r + 2)/((r + 2)(2r + 1)) for even r and (5r + 1)/((dr + 1)(2r + 1)) for odd r. The optimal density of a (1, less than or equal to 2)-identifying code in the infinite hexagonal mesh is shown to be 2/3 and the optimal densities of (1, less than or equal to 3)- and (2, less than or equal to 3)-identifying codes are shown to be 1. (C) 2003 Elsevier B.V. All rights reserved.
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