A New Class of Pyramidally Solvable Symmetric Traveling Salesman Problems
SIAM Journal on Discrete 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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem
INFORMS Journal on Computing
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Traveling salesman games with the Monge property
Discrete Applied Mathematics
The maximum traveling salesman problem on van der Veen matrices
Discrete Applied Mathematics
An approximation algorithm for a bottleneck traveling salesman problem
Journal of Discrete Algorithms
Fast minimum-weight double-tree shortcutting for metric TSP: Is the best one good enough?
Journal of Experimental Algorithmics (JEA)
On the optimality of spiral search
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Using well-solvable quadratic assignment problems for VLSI interconnect applications
Discrete Applied Mathematics
One-Sided monge TSP is NP-Hard
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
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In most of the known polynomially solvable cases of the symmetric travelling salesman problem (TSP) which result from restrictions on the underlying distance matrices, the restrictions have the form of so-called four-point conditions (the inequalities involve four cities). In this paper we treat all possible (symmetric) four-point conditions and investigate whether the corresponding TSP can be solved in polynomial time. As a by-product of our classification we obtain new families of exponential neighborhoods for the TSP which can be searched in polynomial time and for which conditions on the distance matrix can be formulated so that the search for an optimal TSP solution can be restricted to these exponential neighborhoods.