矩陣轉換網路

Abstract

在現代，多級式交換網路已經越來越重要了，它常常被用來討論電話網路上的阻塞問題。最常見的就是 baseline 網路、banyan 網路及 shuffle exchange 網路。有時候，大家會把看似不同實則一樣的網路結構重覆討論，所以最近有很多研究就是在如何將這些網路做一個分類。張、黃和董利用位元重排網路將這些典型的網路分類，簡化為一個正整數的數列，我們則將網路用矩陣轉換的方式做連結，來得到一個更大集合的網路，並將他們做完整的分類。

In this modern age, multistage interconnection networks become more and more important. One of the main issue is about the nonblocking property of networks. Typical examples of networks include baseline, banyan, and shuffle exchange networks. there are many research on these networks. A popular topic is to characterize them, as people often study the same but look-different network repeatedly. Chang, Hwang and Tong studied bit permutation networks which give these networks a mathematical view, and characterize them by sequences of integers. The attempt of this thesis is to investigate more networks. We discuss the networks in a more general setting by connection the networks using affine transformation functions.