P-Complete Approximation Problems
Journal of the ACM (JACM)
Theoretical Computer Science
The Traveling Salesman Problem with flexible coloring
Discrete Applied Mathematics
32-approximation algorithm for two variants of a 2-depot Hamiltonian path problem
Operations Research Letters
A 53-approximation algorithm for the clustered traveling salesman tour and path problems
Operations Research Letters
An improved approximation algorithm for the clustered traveling salesman problem
Information Processing Letters
Eight-Fifth approximation for the path TSP
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
GRASP with path relinking for the symmetric Euclidean clustered traveling salesman problem
Computers and Operations Research
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For the traveling salesman problem in which the distances satisfy the triangle inequality, Christofides' heuristic produces a tour whose length is guaranteed to be less than 32 times the optimum tour length. We investigate the performance of appropriate modifications of this heuristic for the problem of finding a shortest Hamiltonian path. There are three variants of this problem, depending on the number of prespecified endpoints: zero, one, or two. It is not hard to see that, for the first two problems, the worst-case performance ratio of a Christofides-like heuristic is still 32. For the third case, we show that the ratio is 53 and that this bound is tight.