A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
Upper bounds on ATSP neighborhood size
Discrete Applied Mathematics
Dendrogram seriation using simulated annealing
Information Visualization
Further Extension of the TSP Assign Neighborhood
Journal of Heuristics
Good triangulations yield good tours
Computers and Operations Research
Approximating the Metric TSP in Linear Time
Graph-Theoretic Concepts in Computer Science
Fast minimum-weight double-tree shortcutting for metric TSP: Is the best one good enough?
Journal of Experimental Algorithmics (JEA)
Fast minimum-weight double-tree shortcutting for metric TSP
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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Let D = (dij) be the n × n distance matrix of a set of n cities {1, 2,...,n}, and let T be a PQ-tree with node degree bounded by d that represents a set Π(T) of permutations over {1, 2,...,n}. We show how to compute for D in O(2dn3) time the shortest travelling salesman tour contained in Π(T). Our algorithm may be interpreted as a common generalization of the well-known Held and Karp dynamic programming algorithm for the TSP and of the dynamic programming algorithm for finding the shortest pyramidal TSP tour. A consequence of our result is that the shortcutting phase of the "twice around the tree" heuristic for the Euclidean TSP can be optimally implemented in polynomial time. This contradicts a statement of Papadimitriou and Vazirani as published in 1984.