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

Research output: Contribution to journalArticle

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

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salesman
Traveling salesman problem
Travelling salesman problems
Analogue
Polynomials
Polynomial time
Class
time

Keywords

  • A pyramidal tour
  • Polynomially solvable classes
  • Traveling salesman

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modelling and Simulation
  • Transportation

Cite this

An asymmetric analog of van der Veen conditions and the traveling salesman problem (II). / Oda, Yoshiaki.

In: European Journal of Operational Research, Vol. 138, No. 1, 01.04.2002, p. 43-62.

Research output: Contribution to journalArticle

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