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

Jun Wu (), Zhen Yang (), Guiqing Zhang () and Yongxi Cheng ()
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Jun Wu: Xi’an Jiaotong University
Zhen Yang: Xi’an Jiaotong University
Guiqing Zhang: Xi’an Jiaotong University
Yongxi Cheng: Xi’an Jiaotong University

Journal of Combinatorial Optimization, 2024, vol. 47, issue 2, No 6, 11 pages

Abstract: 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 .

Keywords: Approximation ratio; Christofides heuristic; Multiple Hamiltonian path problem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-023-01104-8

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