基于Cayley图的三维六度环面网络研究  

Research on 3D Hexagonal Torus Based on Cayley Graph

作　　者：张震[1] 肖文俊[2] 黄书强[3] 

机构地区：[1]暨南大学计算机科学与技术系,广东广州510632 [2]华南理工大学软件学院,广东广州510641 [3]暨南大学网络与教育技术中心,广东广州510632

出　　处：《软件学报》2015年第7期1584-1600,共17页Journal of Software

基　　金：国家自然科学基金(60973150;61272073;61373125;61170313;61103037;61370003);国家高技术研究发展计划(863)(2013AA040404);广东省自然科学基金(2014A030313386);广东省教育厅科技创新项目(2013KJCX0018);暨南大学科研培育与创新基金(21615439;21615443)

摘　　要：提出了一种三维六度环面Cayley图网络模型.针对该网络模型,给出了一种简单的三维节点编址方案,并利用该编址方案得到了任意两个节点间的最短距离公式;开发了一种简单的分布式最优路由算法,该算法可以运行于网络中的任意节点,可以建立任意两点之间的最短路由路径;基于陪集图(coset graph)理论,给出了一种新型的广播通信算法,并对该算法的效率进行了分析;给出了三维六度环绕网络模型直径的界限值.The 3D hexagonal toms is presented as a natural extension of the hexagonal toms. Hexagonal tori are proved to be a type of Cayley graph. This paper develops a new type of 3D hexagonal torus based on Cayley graph. An addressing scheme for this type of network is developed. Based on this addressing scheme, the distance formula between any two nodes is derived. Then, a distributed optimal routing algorithm is developed. This distributed routing algorithm is optimal, which means it can be executed on any node in the network to construct a shortest path between any pair of nodes. A broadcasting algorithm is also presented according to the coset graph theory. The upper bound and lower bound of the diameter are also proposed in this paper.

关 键 词：互连网络 CAYLEY图 六度环面网络 两点间最短距离 通信算法 网络直径 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]