加权互斥最大集合覆盖问题的精确算法

Exact algorithms for weighed mutually exclusive maximum set cover problem

加权互斥最大集合覆盖问题是一个NP难问题,为解决该问题设计一个分支搜索算法,采用测量治之方法对算法运行时间界进行分析,得到算法的时间复杂度为O^*(1.3132 m),改进该问题原有的最佳运行时间界O^*(1.325 m)。通过比较可知,基于测量治之方法分析得到的结果优于传统方法分析得到的结果,可以在不改变算法的前提下通过度量设置的改变进一步改进算法的运行时间界,度量设置方案越详细得到的结果更好。

The weighted mutually exclusive maximal set cover problem is a NP-hard problem.To solve this problem,a branch and reduce algorithm was designed and it was analyzed using the measure-and-conquer method.Its running time bound was O^*(1.3132 m)which improved the original best running time bound O^*(1.325 m)for this problem.The comparison shows that the result obtained using the measure-and-conquer method is better than that obtained by the traditional method.Through the measure-and-conquer method,the algorithm running time bound can be further improved by changing the measure settings without changing the original algorithm,and the scheme of measure settings is more detailed and the results obtained are better.