基于搜索树的平面图支配集算法

摘要

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)n°(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.