有限集上构建拓扑的集簇式递推算法
Recursive Algorithm to Construct Topologies on a Finite Set
-
摘要: 为了解决有限集上的拓扑计数问题,对拓扑的结构性质进行了分析研究;针对穷举法中庞大的计算量,提出了一种集簇式递推算法,以n-1元集合的拓扑为基础,以扩展子集为线索来构建n元集合的拓扑;与传统的穷举法相比,大大降低了时间复杂度,减少了计算时间,并通过实验验证了算法的有效性.Abstract: This study focuses on the solution to the topologies counting problem on a finite set from the perspective of topological structure properties.Based on the topologies on a set of n-1 elements,a recursive algorithm which constructs the topologies on a set of n elements is put forward following the extended subset.Compared with the traditional method,the algorithm expedites and simplifies the computing.Most importantly,its effectiveness has been verified through experiments.