互连网络的新模型:多部群论模型

发布时间：2018-03-18 07:43

本文选题：互连网络　切入点：星网络　出处：《计算机科学》2013年09期 　论文类型：期刊论文

【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。
[Abstract]:Interconnection network is an important part of supercomputer. Interconnect network determines the performance of supercomputer to a great extent. In 1989, S.B.Akers et al put forward the group theory model of interconnection network, and designed the star network according to the model. A large number of networks, such as bubbling sorting networks, especially star networks, have a lot of good performance and are considered a substitute for hypercubes. But they all have a weakness: network size (number of nodes) is n! That is, with the increase of n! The speed of growth is too fast, so it is more difficult to upgrade the supercomputer based on the network structure, that is, the expansibility is poor. On the basis of the group theory model, the multipart group theory model of the interconnection network is proposed, and then the multipart group theory model of the interconnection network is proposed. Based on this model, several kinds of networks are designed, such as several star networks, many bubble sorting networks and so on. It is proved that the star network is a network of nnn ~ (1) and multi-star, and that the scale (number of nodes) and the increase of diameter of the network are fixed, and the diameter of the network increases slowly. The node degree is constant, that is, it has good scalability, and other networks have similar performance.
【作者单位】：西北师范大学数学与统计学院;
【基金】：甘肃省自然科学基金(ZS991-A25-017-G)资助
【分类号】：TP393.0

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