The Traveling Salesman Problem in Circulant Weighted Graphs With Two Stripes

  • Authors:

  • Federico Greco;Ivan Gerace

  • Affiliations:

  • Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy;Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2007

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Abstract

The Symmetric Circulant Traveling Salesman Problem asks for the minimum cost of a Hamiltonian cycle in a circulant weighted undirected graph. The computational complexity of this problem is not known. Just a constructive upper bound, and a good lower bound have been determined. This paper provides a characterization of the two stripe case. Instances where the minimum cost of a Hamiltonian cycle is equal either to the upper bound, or to the lower bound are recognized. A new construction providing Hamiltonian cycles, whose cost is in many cases lower than the upper bound, is proposed for the remaining instances.