三环网络G(N;s_1,s_2,s_3)的直径及其紧优性

Diameter and tight optimal of triple-loop networks G(N;s_1,s_2,s_3)

根据三环网络的拓扑结构,利用等价树的思想构造出三环网络的最小路径图.研究了等价树的相关性质,以及三环网络的信息传输的最小延迟与等价树层之间的关系,并给出了三环网络直径的计算方法.利用计算机搜索,找到了大量的紧优三环网络,并与紧优双环网络进行了对比,给出了紧优三环网络的分布特性.验证了Aguiló-Gost所给出的三环网络直径的下界.

According to the topology structure of the triple-loop networks G（N;s1,s2,s3） and the idea of the equivalent tree, a minimum distance diagram of the triple loop networks was introduced. Characteristic of the equivalent tree was studied, and relationship between the layer of the equivalent tree and the minimum transmission delay about message of triple loop networks was found. Thus, the method to compute the diameter of triple loop networks was given. By computer searching, lots of tight optimal triple loop networks were found, by comparison tight optimal between the double loop networks and the triple loop networks, the distribution about the tight optimal triple loop networks was represented. Finally, the limited bound of the diameter of the triple loop networks presented by Aguiló-Gost was verified.