For a given graph G, the minimum weight connected-k-subgraph cover problem (MinWCkSC) is to find a minimum weight vertex subset C of G such that each connected subgraph of G on k vertices contains at least one vertex of C. Previously, Zhang et al. [37] presented a $(k-1)$-approximation algorithm for MinWCkSC under the assumption that the girth of G, which is the length of a shortest cycle of G, is at least k. In this paper, we improve this result by showing that $(k-1)$-approximation can be achieved when the girth requirement is relaxed from k to $2k/3$.

中文翻译：

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为最小重量connected-近似算法ķ -subgraph盖

对于给定的图G，最小权重连接的k个子图覆盖问题（MinWC k SC）是找到G的最小权重顶点子集C，以使k个顶点上G的每个连接子图都包含C的至少一个顶点。此前，Zhang等。[37]提出了一个$（ķ-\mathrm{1个}）$近似算法为MinWC ķ假设的周长下SC ģ，这是最短的周期的长度ģ，是至少ķ。在本文中，我们通过显示$（ķ-\mathrm{1个}）$-当周长要求从k放宽到$2ķ/3$。