Traveling salesman games with the Monge property
Discrete Applied Mathematics
On the euclidean TSP with a permuted Van der Veen matrix
Information Processing Letters
Four point conditions and exponential neighborhoods for symmetric TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Theoretical Computer Science
Pyramidal tours and multiple objectives
Journal of Global Optimization
One-Sided monge TSP is NP-Hard
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
A new asymmetric pyramidally solvable class of the traveling salesman problem
Operations Research Letters
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An instance of the symmetric traveling salesman problem (STSP) is pyramidally solvable if there is a shortest tour that is pyramidal. A pyramidal tour is a Hamiltonian tour that consists of two parts; according to the labeling of the vertices in the first part the vertices are visited in increasing order and in the second part in decreasing order. It is well known that a shortest pyramidal tour can be found in ${\cal O}(n^2)$ time. In this paper it is shown that the STSP restricted to the class of distance matrices is pyramidally solvable. Furthermore, it is shown that ${\Bbb D}_{NEW} \not\subset {\Bbb D}_{DEMI}$, i.e., that ${\Bbb D}_{NEW}$ is not contained in the class of symmetric Demidenko matrices ${\Bbb D}_{DEMI}$ that was, until now, the most general class of pyramidally solvable STSPs. It is also shown that ${\Bbb D}_{DEMI} \not\subset {\Bbb D}_{NEW}$.