Given a weighted graph $G$ with $n$ vertices and $m$ edges, and a positive integer $p$, the Hamiltonian $p$-median problem consists in finding $p$ cycles of minimum total weight such that each vertex of $G$ is in exactly one cycle. We introduce an $O(n^6)$ 3-approximation algorithm for the particular case in which $p \leq \lceil \frac{n-2\lceil \frac{n}{5} \rceil}{3} \rceil$. An approximation ratio of 2 might be obtained depending on the number of components in the optimal 2-factor of $G$. We present computational experiments comparing the approximation algorithm to an exact algorithm from the literature. In practice much better ratios are obtained. For large values of $p$, the exact algorithm is outperformed by our approximation algorithm.

翻译：考虑到一个带有美元脊椎和美元边缘的加权图表$G$,加上正整数美元,汉密尔顿美元中中位问题在于找到最低总重量的p美元周期,这样每顶峰$G美元就完全处于一个周期。我们为特定案例引入了一个3美元3个准比算法,即$p\leq\lceil{n-2\lcil}\frac{n\lcil}{n ⁇ 5}\rceil}}3}\rceil$。近似比率为2,这取决于最优2个基数$的组件数量。我们提出计算实验,将近似算法与文献中精确的算法进行比较。在实践上,得到的比率要好得多。对于大数值$p$,精确算法比我们的近似算法差得多。