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

Research output: Contribution to journalArticle

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

Fingerprint

Traveling salesman problem
Travelling salesman problems
Polynomials
Analogue
Polynomial time
Class

Keywords

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

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

An asymmetric analogue of van der Veen conditions and the traveling salesman problem. / Oda, Yoshiaki.

In: Discrete Applied Mathematics, Vol. 109, No. 3, 15.05.2001, p. 279-292.

Research output: Contribution to journalArticle

@article{121348b7476149118096e062d560d0cc,
title = "An asymmetric analogue of van der Veen conditions and the traveling salesman problem",
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.",
keywords = "A pyramidal tour, Polynomially solvable classes, The traveling salesman problem",
author = "Yoshiaki Oda",
year = "2001",
month = "5",
day = "15",
doi = "10.1016/S0166-218X(00)00273-0",
language = "English",
volume = "109",
pages = "279--292",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - An asymmetric analogue of van der Veen conditions and the traveling salesman problem

AU - Oda, Yoshiaki

PY - 2001/5/15

Y1 - 2001/5/15

N2 - 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.

AB - 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.

KW - A pyramidal tour

KW - Polynomially solvable classes

KW - The traveling salesman problem

UR - http://www.scopus.com/inward/record.url?scp=0007705353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007705353&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(00)00273-0

DO - 10.1016/S0166-218X(00)00273-0

M3 - Article

AN - SCOPUS:0007705353

VL - 109

SP - 279

EP - 292

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 3

ER -