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.
- A pyramidal tour
- Polynomially solvable classes
- The traveling salesman problem
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics