中文摘要：

部分控制集问题是对于给定的顶点赋权图G=（V，E；c）和正整数K，寻找图G-个顶点子集丁，使得在其控制下的顶点个数不小于K且T中顶点权和达到最小。本文讨论了部分控制集问题的NP-困难性；给出了该问题的一种修正Greedy近似算法，并对其近似度H（K）给出了证明。

英文摘要：

In this paper a kind of partial dominating set problems is discussed- given a vertex weighted graph G=（V,E;c） and a positive number K, the objective is to find a subset T∩V such that at least K vertices of V are dominated by T and the total vertex weight of T is minimized. First, the partial dominating set problem is shown to be NP-hard. Then a revised Greedy algorithm is proposed, which is proved to have the performance ratio H（K）.