Exact minimum density of codes identifying vertices in the square grid

Yael Ben-Haim; Simon Litsyn

doi:10.1137/S0895480104444089

Exact minimum density of codes identifying vertices in the square grid

Yael Ben-Haim^*, Simon Litsyn

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

An identifying code C is a subset of the vertices of the square grid ℤ² with the property that for each element v of ℤ², the collection of elements from C at a distance of at most one from v is nonempty and distinct from the collection of any other vertex. We prove that the minimum density of C within ℤ² is 7/20.

Original language	English
Pages (from-to)	69-82
Number of pages	14
Journal	SIAM Journal on Discrete Mathematics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1137/S0895480104444089
State	Published - 2005

Keywords

Density
Graph
Identifying code
Square grid

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10.1137/S0895480104444089

Cite this

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Exact minimum density of codes identifying vertices in the square grid

Abstract

Keywords

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