Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
The Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Introduction to algorithms
Four point conditions and exponential neighborhoods for symmetric TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast minimum-weight double-tree shortcutting for metric TSP
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Match twice and stitch: a new TSP tour construction heuristic
Operations Research Letters
Parameterized Complexity
A probabilistic analysis of christofides' algorithm
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within, at most, a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, that is, the minimum-weight double-tree shortcutting. Burkard et al. gave an algorithm for this problem, running in time O(n3 + 2d n2) and memory O(2d n2), where d is the maximum node degree in the rooted minimum spanning tree. We give an improved algorithm for the case of small d (including planar Euclidean TSP, where d ≤ 4), running in time O(4d n2) and memory O(4d n). This improvement allows one to solve the problem on much larger instances than previously attempted. Our computational experiments suggest that in terms of the time-quality trade-off, the minimum-weight double-tree shortcutting method provides one of the best existing tour-constructing heuristics.