In this paper, we study a multiple-terminal extension of the classic Hamiltonian path problem where $m$ salesmen are initially located at different depots and finally stopped at different terminals. To the best of our knowledge, only 2-approximation algorithm is available in the literature. For arbitrary $m⩾2$, we first present a Christofides-like heuristic with a tight approximation ratio of $2-\frac{1}{2m+1}$. Besides, we also develop a $(\frac{5}{3}+ϵ)$-approximation algorithm by divide-and-conquer technique. The $(\frac{5}{3}+ϵ)$-approximation algorithm runs in polynomial time for fixed $m$ and $ϵ$.

中文翻译：

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逼近多仓库多终端哈密顿路径问题

在本文中，我们研究了经典哈密顿路径问题的多端扩展，其中 $米$销售人员最初位于不同的仓库，最后停在不同的终端。据我们所知，文献中仅提供2种近似算法。对于任意$米⩾2$，我们首先提出一种类似Christofides的启发式方法，其近似比率为 $2-\frac{\mathrm{1个}}{2米+\mathrm{1个}}$。此外，我们还开发了$（\frac{5}{3}+ϵ）$分而治之的近似算法。的$（\frac{5}{3}+ϵ）$-近似算法在多项式时间内运行以进行固定 $米$ 和 $ϵ$。