An asymmetric analogue of van der Veen conditions and the traveling salesman problem

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4 Citations (Scopus)

Abstract

In (J.A.A. van der Veen, SIAM J. Discrete Math, 7, 1994, 585-592), van der Veen proved that for the traveling salesman problem which satisfies some symmetric conditions (called van der Veen conditions) a shortest pyramidal tour is optimal. From this fact, an optimal tour can be computed in polynomial time. In this paper, we prove that a class satisfying an asymmetric analogue of van der Veen conditions is polynomially solvable. An optimal tour of the instance in this class forms a tour which is an extension of pyramidal ones.

Original languageEnglish
Pages (from-to)279-292
Number of pages14
JournalDiscrete Applied Mathematics
Volume109
Issue number3
DOIs
Publication statusPublished - 2001 May 15

Keywords

  • A pyramidal tour
  • Polynomially solvable classes
  • The traveling salesman problem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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