半边图模型之聚合归约演算

Aggregation and Reduction Calculus of Half Edge Graph

提出了实现自组织多层次归约的一个指导原则,即自组聚合与归约的协调准则,其核心思想是,基于多聚合准则的自组聚合演算中的各个聚合子集是可以相交的,相交的部分是下一步归约演算的基础。给出了符合上述协调准则的自组图聚合归约演算模型,聚合子图是聚合演算的结果,在归约演算中,聚合子图对应为归约顶点,子图的子边界对应为归约半边,而由子图相交部分抽象出的子图边界之间的关系则对应为归约边,从而构成了形式上完整统一的自组织多层次归约。

A generality guide principle for reduction with hierarchical self-organization is proposed.That is the coordination criterion for self-organizing aggregate process and reduce process.The core thinking is,the various aggregation subsets based upon the self-organizing aggregation calculus with diversified aggregation criterion could have the intersect parts.These intersect parts are the foundation for the reduction calculus which followed the aggregation calculus.Then,a self-organizing aggregation calculus model for self-organization graph is given.These calculi model is in keeping with the coordination criterion for self-organizing aggregate process and reduce process.The aggregate sub graphs are the outcome of the self-organizing aggregation calculus.The mutual relations among the sub graphs could deduce from the sub metes of the sub graphs.The most important calculus model i.e.the reduction calculus model is given.In this model ,the aggregate sub graph reduces to the reduction vertex one on one ,the sub mete of the sub graph reduces to the reduction half edge one on one also,and the mutual relation between the two sub graphs reduces to the reduction edge.Therefore,a formal unity reduction with hierarchical self-organization comes to realize.