On the traveling salesman problem in binary hamming spaces

Gérard Cohen, Simon Litsyn, Gilles Zémor

Research output: Contribution to journalArticlepeer-review

Abstract

Given a subset X of vertices of the n-cube (i.e., the n-dimensional Hamming space), we are interested in the solution of the traveling salesman problem; namely, the minimal length of a cycle passing through all vertices of X. For a given number M, we estimate the maximum of these lengths when X ranges over all possible choices of sets of M vertices. Asymptotically, our estimates show that for a number M of vertices growing exponentially in n, the maximum is attained for a code with maximal possible minimum distance.

Original languageEnglish
Pages (from-to)1274-1276
Number of pages3
JournalIEEE Transactions on Information Theory
Volume42
Issue number4
DOIs
StatePublished - 1996

Keywords

  • Data compression
  • Gray codes
  • Minimal cycle
  • Traveling salesman

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