A New Class of Pyramidally Solvable Symmetric Traveling Salesman Problems
SIAM Journal on Discrete Mathematics
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
On the traveling salesman problem with a relaxed Monge matrix
Information Processing Letters
The maximum travelling salesman problem on symmetric Demidenko matrices
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Optimal covering tours with turn costs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Hamiltonian Cycles in Solid Grid Graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The maximum traveling salesman problem on van der Veen matrices
Discrete Applied Mathematics
Four point conditions and exponential neighborhoods for symmetric TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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The Travelling Salesman Problem (TSP) is a classical NP-hard optimisation problem. There exist, however, special cases of the TSP that can be solved in polynomial time. Many of the well-known TSP special cases have been characterized by imposing special four-point conditions on the underlying distance matrix. Probably the most famous of these special cases is the TSP on a Monge matrix, which is known to be polynomially solvable (as are some other generally NP-hard problems restricted to this class of matrices). By relaxing the four-point conditions corresponding to Monge matrices in different ways, one can define other interesting special cases of the TSP, some of which turn out to be polynomially solvable, and some NP-hard. However, the complexity status of one such relaxation, which we call one-sided Monge TSP (also known as the TSP on a relaxed Supnick matrix), has remained unresolved. In this note, we show that this version of the TSP problem is NP-hard. This completes the full classification of all possible four-point conditions for symmetric TSP.