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An extension of the Christofides heuristic for a single-depot multiple Hamiltonian path problem

Author

Listed:
  • Jun Wu

    (Xi’an Jiaotong University
    IBISC, Univ Évry, University of Paris-Saclay)

  • Zhen Yang

    (Xi’an Jiaotong University
    Xi’an Jiaotong University
    State Key Lab for Manufacturing Systems Engineering)

  • Guiqing Zhang

    (Xi’an Jiaotong University)

  • Yongxi Cheng

    (Xi’an Jiaotong University
    State Key Lab for Manufacturing Systems Engineering)

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 $$2-1/(2+k)$$ 2 - 1 / ( 2 + k ) with $$O(n^3)$$ O ( n 3 ) running time for arbitrary $$k\ge 1$$ k ≥ 1 .

Suggested Citation

  • Jun Wu & Zhen Yang & Guiqing Zhang & Yongxi Cheng, 2024. "An extension of the Christofides heuristic for a single-depot multiple Hamiltonian path problem," Journal of Combinatorial Optimization, Springer, vol. 47(2), pages 1-11, March.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:2:d:10.1007_s10878-023-01104-8
    DOI: 10.1007/s10878-023-01104-8
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    References listed on IDEAS

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    1. Zhou Xu & Brian Rodrigues, 2015. "A 3/2-Approximation Algorithm for the Multiple TSP with a Fixed Number of Depots," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 636-645, November.
    2. Min Li, 2022. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1693-1704, October.
    3. Songhua Li & Minming Li & Lingjie Duan & Victor C. S. Lee, 2022. "Online algorithms for the maximum k-interval coverage problem," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3364-3404, December.
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