Exact minimum density of codes identifying vertices in the square grid

Yael Ben-Haim, Simon Litsyn

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)69-82
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Volume19
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Density
  • Graph
  • Identifying code
  • Square grid

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