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 |
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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 |
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