We provide a simple and novel algorithmic design technique, for which we call iterative partial rounding, that gives a tight rounding-based approximation for vertex cover with hard capacities (VC-HC). In particular, we obtain an f-approximation for VC-HC on hypergraphs, improving over a previous results of Cheung et al. (In: SODA’14, 2014) to the tight extent. This also closes the gap of approximation since it was posted by Chuzhoy and Naor (Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS) 2002, pp. 481--489. IEEE Computer Society, 2002). Our main technical tool for establishing the approximation guarantee is a separation lemma that certifies the existence of a strong partition for solutions that are basic feasible in an extended version of the natural LP. We believe that our rounding technique is of independent interest when hard constraints are considered.

中文翻译：

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具有硬容量的顶点覆盖的迭代部分舍入

我们提供了一种简单而新颖的算法设计技术，我们将其称为迭代部分舍入，它为具有硬容量的顶点覆盖（VC-HC）提供了基于严格舍入的近似值。特别是，我们在超图上获得了 VC-HC 的 f 近似值，比 Cheung 等人之前的结果有所改进。（在：SODA'14, 2014）到严格的程度。这也缩小了近似值的差距，因为它是由 Chuzhoy 和 Naor 发布的（Proceedings of the 43rd Symposium on Foundations of Computer Science (FOCS) 2002, pp. 481--489. IEEE Computer Society, 2002）。我们用于建立近似保证的主要技术工具是一个分离引理，它证明了在自然 LP 的扩展版本中基本可行的解决方案的强分区的存在。