本文選題：互連網(wǎng)絡 + 并行計算�。� 參考：《中國科學技術大學》2013年博士論文

【摘要】：互連網(wǎng)絡在并行計算和通信系統(tǒng)中發(fā)揮著重要作用.網(wǎng)絡的容錯性是評價互連網(wǎng)絡性能的關鍵指標,它主要考慮在網(wǎng)絡發(fā)生故障的時候網(wǎng)絡中某些特有性質的保持能力.本文主要以圖論作為工具研究故障出現(xiàn)時網(wǎng)絡保持三種性質的能力：多對多不交長路存在性,連通分支最小度,連通分支子網(wǎng)絡結構.在研究中,本文利用高對稱網(wǎng)絡在不同維度上分解的等價性,探索出一套分析網(wǎng)絡容錯性的有效方法,解決了幾個懸而未決的問題. 本文第一章介紹所考慮問題的研究背景以及文章用到的圖論主要概念. 本文第二章主要考慮出現(xiàn)頂點故障超立方體Qn中的k條多對多不交路問題.在考慮條件容錯的前提下,證明故障點數(shù).f不超過2n-2k-3時,對于Qn中在不同部的兩個k-點集合S與T,存在至少含有2n-2f頂點的k條頂點不交的無故障路連接S與T.這個結果改進了很多已知的結論. 本文的第三、四章主要分析類超立方體和星圖的容錯性能.理論上講,類超立方體和星圖具備成為互連網(wǎng)絡拓撲結構的很好潛質,是超立方體的強有力的競爭網(wǎng)絡.本文在第三章中確定了類超立方的高階限制邊連通度和高階嵌入限制邊連通度,對于點的情形確定了超立方體、Mobius立方、交叉超立方體的高階限制連通度和高階嵌入限制連通度.本文在第四章確定了星圖網(wǎng)絡的高階限制點(邊)連通度和高階嵌入限制點(邊)連通度,其中對星圖高階限制點連通度的確定證實了同行學者提出的猜想. 本文的第五、六章主要分析廣義星圖網(wǎng)絡和交換超立方體的高階限制連通性.廣義星圖網(wǎng)絡是星圖的網(wǎng)絡的推廣,它的變化更加靈活,受到了很多學者的關注.交換超立方體是超立方體的另外一種變形,它由超立方體系統(tǒng)的刪去一些邊得到,具有一些很好的性質,同時降低了連接復雜性.本文在第五、六章分別確定廣義星圖網(wǎng)絡和交換超立方體的高階限制點連通度和高階限制邊連通度.
[Abstract]:Interconnection networks play an important role in parallel computing and communication systems. The fault tolerance of network is the key index to evaluate the performance of interconnection network. It mainly considers the maintenance ability of some special properties of the network when the network fails. In this paper, graph theory is used as a tool to study the ability of the network to maintain three properties when faults occur: the existence of many-to-many disjoint long paths, the minimum degree of connected branches, and the network structure of connected branches. In this paper, a set of effective methods to analyze the fault tolerance of high symmetric networks are explored by using the equivalence of decomposition in different dimensions. In the first chapter, we introduce the research background of the problem under consideration and the main concepts of graph theory used in this paper. In the second chapter, we mainly consider the problem of multi-to-many disjoint paths in the hypercube Qn with vertex fault. Considering the condition of fault tolerance, it is proved that when the number of fault points. F is not more than 2n-2k-3, for the set S and T of two k-points in different parts of Qn, there exists at least a disjoint of k vertices with 2n-2f vertices to join S and T. This result improves many known conclusions. In the third and fourth chapters, we analyze the fault-tolerant performance of hypercubes and star graphs. Theoretically, hypercubes and star maps have the potential to become topology of interconnection networks, and are powerful competitive networks of hypercubes. In chapter 3, we determine the high order restricted edge connectivity and high order embedded restricted edge connectivity of hypercubes. For the case of points, we determine the high order restricted connectivity and high order embedded restricted connectivity of cross hypercubes. In chapter 4, we determine the connectivity of high order restricted points (edges) and high order embedded restricted points (edges) of star graph networks. The determination of connectivity of high order restricted points of star graphs proves the conjecture put forward by some scholars. In chapter six, we analyze the high order restricted connectivity of generalized star graph networks and commutative hypercubes. Generalized star map network is a generalization of star map network. Commutative hypercube is another kind of deformation of hypercube. It is obtained by deleting some edges of hypercube system. It has some good properties and reduces the connection complexity. In the fifth and sixth chapters, we determine the connectivity of higher-order restricted points and higher-order restricted edge connectivity of generalized star graph networks and commutative hypercubes, respectively.
【學位授予單位】：中國科學技術大學
【學位級別】：博士
【學位授予年份】：2013
【分類號】：O157.5;TP302.8

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本文編號：1992585