AI 中文总结
该研究通过适配度量旅行商问题的最大熵分布采样技术，得到了近似比严格小于3/2的乡村邮递员问题近似算法，还证明度量TSP的α-近似算法可导出乡村邮递员问题的(α+ε)-近似算法。
AI 中文摘要
我们提出了一种乡村邮递员问题的近似算法，其近似比严格小于3/2。我们通过将Karlin、Klein与Oveis Gharan提出的、针对度量旅行商问题的最大熵分布采样技术适配到乡村邮递员问题，得到了这一结果。我们还发现，对于任意固定的ε>0，任何度量旅行商问题的α-近似算法都能导出乡村邮递员问题的(α+ε)-近似算法；这一推论已隐含在Lampis关于旅行商问题不可近似性的研究中对必须遍历的边的处理里。
英文摘要
We give an approximation algorithm for the rural postman problem with approximation ratio strictly smaller than $3/2$. We obtain this result by adapting to the rural postman problem the technique of sampling from maximum entropy distributions for the metric traveling salesman problem of Karlin, Klein, and Oveis Gharan. We also observe that, for every fixed $\varepsilon>0$, any $α$-approximation algorithm for the metric traveling salesman problem yields an $(α+\varepsilon)$-approximation algorithm for the rural postman problem; this implication is already implicit in the treatment of edges that must be traversed in the work of Lampis on the inapproximability of the traveling salesman problem.
Comments16 pages, no figures
