许多来自工业应用的优化问题都是NP难问题。确定参数可解FPT作为处理这类问题的另外一种思路,在最近的10多年中受到了广泛的关注。支配集问题是图论中最重要的NP完全的组合优化问题之一，即使对于FPT体系而言，一般图中的支配集问题属于W［2］完全的，意味着不可能设计出复杂度为f(k)no(1)的算法。在本文中，我们考虑在给定的平面图G=（V ,E）中参数化支配集问题，给定参数k，看是否存在大小为k的顶点集合支配图中的其他顶点，当把问题限定在平面图上，这个问题属于确定参数可解。本文给出了基于两组归约规则的搜索树算法，通过使用规约技术化简实例，构造搜索树，得到了复杂度为O(8kn)的算法，同时通过相关实验结果显示了归约规则对算法的作用。

The dominating set in graphs is considered to be among the most important problems in combinatorial optimization, which is NPcomplete. From the viewpoint of FixedParameter Tractable, the problem is known to be W［2］complete for general graphs, which means that it is impossible to design an algorithms solve the problem with running time f(k)no(1).We investigate the version where we are given a planar graph G=(V ,E), a parameter k, and ask for a set of vertices of size at most k that dominate all other vertices. It is known to be fixedparameter tractable when restricted to a planar graph. We also give a search tree algorithm based on the two sets of reduction rules and the experiments to show the efficiency between different sets of reduction rules.