Abstract
We study a generalization of the classical Hamiltonian path problem, where multiple salesmen are positioned at the same depot, of which no more than k can be selected to service n destinations, with the objective to minimize the total travel distance. Distances between destinations (and the single depot) are assumed to satisfy the triangle inequality. We develop a non-trivial extension of the well-known Christofides heuristic for this problem, which achieves an approximation ratio of \(2-1/(2+k)\) with \(O(n^3)\) running time for arbitrary \(k\ge 1\).
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Acknowledgements
The authors are grateful to the two anonymous referees for their helpful comments and suggestions which significantly improves the presentation of our paper.
Funding
This work was partially supported by the National Natural Science Foundation of China under Grant No. 71971167, the Major Program of National Natural Science Foundation of China under Grant Nos. 72192830 and 72192834, and China Scholarship Council No. 202206280182.
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Wu, J., Yang, Z., Zhang, G. et al. An extension of the Christofides heuristic for a single-depot multiple Hamiltonian path problem. J Comb Optim 47, 7 (2024). https://doi.org/10.1007/s10878-023-01104-8
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DOI: https://doi.org/10.1007/s10878-023-01104-8