在一個網路系統上傳遞訊息是主要的工作之一，而維護一個網路系統在出現損壞的時候依舊能夠傳遞訊息也是一個相當重要的工作。假設一個雙迴圈網路系統有一個損壞的點，除了最佳路徑的選擇之外，我們試著找尋與最佳路徑完全不相交的次最佳路徑幫助我們作容錯路徑的選擇，因為這樣的一個次最佳路徑可以防止當最佳路徑無法連結時，依然可以保持點與點之間的連結。

Message routing is a fundamental function of a network, and fault-tolerance is an important tool to ensure the quality of service of a network. Assume that network contain only one faulty
element. In order to ensure the message can be arrived. We present a fault-tolerant message routing algorithm which being the secondary path, as the optimal path can't be connected in the
double-loop networks.

1.緒論.....................1
2.參考文獻.................4
2.1雙迴圈上的diameter.....4
2.2多重迴圈上的diameter...7
3.次最佳路徑的搜尋.........11
3.1最佳路徑在第一'三象限..12
3.2最佳路徑在第二象限.....28
3.3最佳路徑在第四象限.....31
4.容錯路徑演算法...........36
4.1當最佳路徑在第一象限...37
4.2當佳路徑在第二象限.....41
4.3當佳路徑在第三象限.....42
4.4當佳路徑在第四象限.....44
4.結論.....................47
reference.................48
A.附錄.....................51
A.1矩形雙重迴圈網路.......52

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