互连网络的新模型:多部群论模型  

New Model for Interconnection Networks:Multipartite Group-theoretic Model

作　　者：师海忠[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《计算机科学》2013年第9期21-24,共4页Computer Science

基　　金：甘肃省自然科学基金(ZS991-A25-017-G)资助

摘　　要：互连网络是超级计算机的重要组成部分。互连网络在很大程度上决定着超级计算机的性能。在1989年,S.B.Akers等提出了互连网络的群论模型,据此模型设计出了星网络、冒泡排序网络等一大批网络。尤其是星网络具有很多很好的性能,被认为是超立方体的替代品。但它们都有一个弱点:网络规模(结点数)为n!。即随着n的增大,n!增速太快,使得据此网络结构设计出的超级计算机升级较为困难,即扩展性较差。在群论模型的基础上提出了互连网络的多部群论模型,进而,据此模型设计出(n,k)-多部星网络、(n,k)-多部冒泡排序网络等多种网络。并证明星网络是(n,1)-多部星网络,而且(n,k)-多部星网络做到了规模(结点数)增大且增幅固定、直径增大缓慢、结点度不变,即有很好的可扩展性,其它(n,k)-多部网络也有类似的性能。An interconnection network is an important partite of a supercomputer. In 1989,8. B. Akers et al, proposed a group-theoretic model for interconnection networks and designed many interconnection networks, such as, star network, bubble sort network, etc. In particularly, star networks own many better performances than the popular n-cubes. How- ever, they have a weakness：the size of all above networks is n!, that is,n! is very speedly increasing with adding of n. This results in that the scalability of supercomputers built by the interconnection networks is very difficult. That is, the scalability of the supercomputer isn＇t good. We proposed a multipartite group-theoretic model based on the the group- theoretic model. By this model, we designed many intercormection networks, such as, （n, k）-multipartite star networks, （n,k）-bubble sort networks, etc. Furthermore, we showed star network is（n, 1）-multipartite star network and（n,k）- multipartite star networks own following better performances：the size of the network increases with fixed increment, its diameter increases slowly, its dgree is fixed. Other（n, k）-multipartite networks designed here own also the perform- ances.

关 键 词：互连网络 星网络 超立方体 （n k）-多部Cayley图 （n k）-多部星网络 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]