TY - JOUR
T1 - An asymmetric analog of van der Veen conditions and the traveling salesman problem (II)
AU - Oda, Yoshiaki
N1 - Funding Information:
The author would like to thank Professors Hikoe Enomoto and Katsuhiro Ota for their helpful suggestions and the referees for their appropriate comments and advice. This work was partially supported by JSPS Research Fellowships for Young Scientists and by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture of Japan.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2002/4/1
Y1 - 2002/4/1
N2 - 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.
AB - 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.
KW - A pyramidal tour
KW - Polynomially solvable classes
KW - Traveling salesman
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U2 - 10.1016/S0377-2217(01)00141-2
DO - 10.1016/S0377-2217(01)00141-2
M3 - Article
AN - SCOPUS:0036532653
VL - 138
SP - 43
EP - 62
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -