在網路上找尋是否嵌含環狀網路，在網路拓樸上是個很基本的問題。已知有許多網路在天生的結構上就含有環狀網路，如立方體網路、網格網路、Be Bruijn 網路、遞迴網路、蝴蝶網路、洗牌-交換網路。然而在洗牌－交換網路上最大嵌含的環狀網路，至今仍然沒有擴張一的答案。本篇論文的主旨，是在洗牌交換網路上找尋嵌含的環狀網路，在本篇提供了一個有效率的演算法來找尋嵌含的環狀網路，在N個處理器的洗牌-交換網路上我們可以找到的最大環狀網路為Q(N/log N)。除此之外，本篇論文提供在洗牌交換網路上尋找大小為k的嵌含環狀網路，如果k <= N/4log N，可以找到最大誤差在 2 lglglgN 之內的嵌入環。

The shuffle-unshuffle-exchange-network (SUEN) was introduced by Stone. It is one of the famous interconnection networks in the filed of parallel processing. In this thesis, we address the problem of embedding rings to SUEN with dilation 1 and load 1. Currently, the size of the largest ring that can be embedded with load 1 and dilation 1 to a SUEN of N processors is still an open problem. We show that given a SUEN of N processors, a ring of theta(N/log N) processors can be imbedded to it with load 1 and dilation 1. Besides, we further show that given any integer k£N/4log N, a ring of k’ processors can be imbedded to a SUEN of N processors with load 1 and dilation 1, where k-2lglglgN<= k’<= k+2lglglgN.

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