An asymmetric analog of van der Veen conditions and the traveling salesman problem (II)

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5 Citations (Scopus)

Abstract

J.A.A. van der Veen [A new class of pyramidally solvable symmetric traveling salesman problems, SIAM J. Discrete Math. 7 (1994) 585-592] proved that for the traveling salesman problem (TSP) which satisfies some symmetric conditions (called van der Veen conditions), a shortest pyramidal tour is optimal, that is, an optimal tour can be computed in polynomial time. In this paper, we prove that a class satisfying an asymmetric analog 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. Moreover, this class properly includes some known polynomially solvable classes.

Original languageEnglish
Pages (from-to)43-62
Number of pages20
JournalEuropean Journal of Operational Research
Volume138
Issue number1
DOIs
Publication statusPublished - 2002 Apr 1
Externally publishedYes

Keywords

  • A pyramidal tour
  • Polynomially solvable classes
  • Traveling salesman

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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