由於近年來光纖佇列理論發展的啟發，在本論文中我們探討一種多級互連網路（MINs），稱螺旋網路。有別於一般遞迴式建構的多級互連網路（二級式展開或者是三級式展開），螺旋網路是直接由一個串接的二分網路來建構。此外，這些二分網路的鄰接矩陣是總合循環位移矩陣冪次方的子集合。雖然多級互連網路在文獻上已被廣泛的研究過，我們證明螺旋網路上幾個較顯著特性，包括可繞行性與有條件的非阻礙性（conditional non-blocking）。特別是我們證明一個滿足本論文(A1)條件式的螺旋網路會是可繞行的，而且在螺旋網路上的封包可以利用在光纖佇列理論裡闡述的C-轉換來達到自尋路由的特性。此外，我們定義一個N-modulo距離用來證明出，若任意兩個輸出阜的N-modulo距離不大於其對應的兩個輸入阜的N-modulo距離，則在一個滿足本論文(A2)條件式的螺旋網路會具有有條件的非阻礙性。這個有條件的非阻礙性可用來證明具有N個輸入/輸出阜的螺旋網路可用來當作任何2≤p≤N的p×p旋轉器(rotator)及p×p對稱分時多工交換機。如此一來我們可以把一個螺旋網路用在一個具有任意數目線路卡的二級式負載平衡交換機上！

Inspired by the recent development of optical queueing theory, in this paper we study a class of multistage interconnection networks (MINs), called twister networks. Unlike the usual recursive constructions of MINs (either by two-stage expansion or by three-stage expansion), twister networks are constructed directly by a concatenation of bipartite networks. Moreover, the biadjacency matrices of these bipartite networks are sums of subsets of the powers of the circular shift matrix. Though MINs have been studied extensively in the literature, we show there are several distinct properties for twister networks, including routability and conditionally nonblocking properties. In particular, we show that a twister network satisfying (A1)in the paper is routable, and packets can be self-routed through the twister network by using the C-transform developed in optical queueing theory. Moreover, we de‾ne an N-modulo distance and use it to show that a twister network satisfying (A2) in the paper is conditionally nonblocking if the N-modulo distance between any two outputs is not greater than two times of the N-modulo distance between the corresponding two inputs. Such a conditionally nonblocking property allows us to show that a twister network with N inputs/outputs can be used as a p £ p rotator and a pxp symmetric TDM switch for any 2 · p · N. As such, one can use a twister network as the switch fabric for a two-stage load balanced switch that is capable of providing incremental update of the number of linecards.

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