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An approximation algorithm for the clustered path travelling salesman problem

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Abstract

In this paper, we consider the clustered path travelling salesman problem. In this problem, we are given a complete graph \(G=(V,E)\) with an edge weight function w satisfying the triangle inequality. In addition, the vertex set V is partitioned into clusters \(V_1,\ldots ,V_k\) and st are two given vertices of G with \(s\in V_1\) and \(t\in V_k\). The objective of the problem is to find a minimum Hamiltonian path of G from s to t, where all vertices of each cluster are visited consecutively. In this paper, we deal with the case that the start-vertex and the end-vertex of the path on each cluster are both specified, and for it we provide a polynomial-time approximation algorithm.

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Acknowledgements

The authors would like to thank the referees for giving this paper a careful reading and many valuable comments and suggestions.

Funding

This work was supported by the NSF of China (No. 11971146), the NSF of Hebei Province of China (Nos. A2019205089, A2019205092), Overseas Expertise Introduction Program of Hebei Auspices (25305008) and the Graduate Innovation Grant Program of Hebei Normal University (No. CXZZSS2022052).

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Correspondence to Wen Liu.

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Zhang, J., Gao, S., Hou, B. et al. An approximation algorithm for the clustered path travelling salesman problem. J Comb Optim 45, 104 (2023). https://doi.org/10.1007/s10878-023-01029-2

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