通过定义判别函数来判别顶点覆盖作用的优劣,得出一个把顶点加入到最小顶点覆盖集的一般化规则,并得出该规则在多种具体情况下的应用定理,在此基础上给出了一个快速降阶算法,该算法能确定某些顶点应该在最小顶点覆盖中,某些顶点不应该在最小顶点覆盖中,达到降低原问题的规模和求解难度的目的.该算法既可以单独使用,又可以与算法结合来达到更好的结果,文中还给出了应用实例及其分析.
By defining the discriminant function that can decide the cover effect of two sets of vertex, a generalized rule that can add vertexes into the set of minimum vertex cover was provide. Based on the generalized rule, many applicable theorems that are the special case of the generalized rule were given. Then a fast reduction algorithm was proposed for minimum vertex cover problem. The algorithm can decide which vertexes should be in the optimal solution and which vertexes should not be, so it can reduce the size and difficulty of the problem. The algorithm not only can be used singly, but also can be combined with other algorithms to get better solutions. Series of examples and instances are solved and analyzed.