An extension of the Christofides heuristic for a single-depot multiple Hamiltonian path problem,Journal of Combinatorial Optimization

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An extension of the Christofides heuristic for a single-depot multiple Hamiltonian path problem
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2024-02-12 , DOI: 10.1007/s10878-023-01104-8
Jun Wu , Zhen Yang , Guiqing Zhang , Yongxi Cheng

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 \(k\ge 1\).

更新日期：2024-02-13

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