二正則有向網路直徑之研究

Abstract

本論文介紹一種新的網路結構，稱為附加式1.5迴圈網路，以及其諸多性質，如連通性，同構性，漢米爾頓性質，容錯性，及最重要的直徑的性質。此種網路與雙環網路皆為二正則有向網路，其差異只在附加式1.5迴圈網路採兩兩相互的鏈結，但卻有使直徑縮短這個突破性的網路性質，故為一值得推廣的網路結構。 另一方面，為了改良附加式1.5迴圈網路在s為偶數時的重覆鏈結，我們改進了部份鏈結，使其在直徑上的縮減相同於s是奇數時的表現。我們更將其從2超節點推廣成k超節點，結果直徑下降到趨近於最佳結果log2N。 最後我們亦呈現一種log2N的二正則有向網路的鏈結方式。

This paper introduces a new network structure, called Mixed 1.5-loop network, and its properties, like connectivity, isomorphic property, harniltonian property, edge-fault tolerant property, and the most important property-diameter. This kind of network and double loop network are both 2-in-2-out regular networks, and the difference of these is the two way links in Mixed 1.5-loop network. However, this kind of network has shorter diameter than double loop network, and thus it is worthy to popularize. On the other hand, in order to improve the double links of Mixed 1.5-loop network with even s, we change the partial links of this network to be the same as odd s in 0(2N) diameter. Moreover, we change two way links to k way links to get O(kN*kk-1) diameter. At last, we also present a 2-in-2-out network of diameter log2N.