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 language | English |
|---|---|
| Pages (from-to) | 43-62 |
| Number of pages | 20 |
| Journal | European Journal of Operational Research |
| Volume | 138 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 Apr 1 |
| Externally published | Yes |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - An asymmetric analog of van der Veen conditions and the traveling salesman problem (II)
AU - Oda, Yoshiaki
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
UR - http://www.scopus.com/inward/record.url?scp=0036532653&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036532653&partnerID=8YFLogxK
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 -