Fault-tolerant locating-dominating sets
Discrete Mathematics
On the density of identifying codes in the square lattice
Journal of Combinatorial Theory Series B
Exact Minimum Density of Codes Identifying Vertices in the Square Grid
SIAM Journal on Discrete Mathematics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
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An r-identifying code in a graph G=(V,E) is a subset C@?V such that for each u@?V the intersection of C and the ball of radius r centered at u is nonempty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the square grid with density 5/29~0.172 and that there are no 2-identifying codes with density smaller than 3/20=0.15. Recently, the lower bound has been improved to 6/37~0.162 by Martin and Stanton (2010) [11]. In this paper, we further improve the lower bound by showing that there are no 2-identifying codes in the square grid with density smaller than 6/35~0.171.