An explicit lower bound for TSP with distances one and two

  • Authors:
  • Lars Engebretsen

  • Affiliations:
  • Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm, Sweden

  • Venue:
  • STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
  • Year:
  • 1999

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Abstract

We show that it is NP-hard to approximate the traveling salesman problem with distances one and two within 5381=5380-Ɛ, for any Ɛ 0. Our proof is a reduction from systems of linear equations mod 2 with two unknowns in each equation and at most three occurrences of each variable.