本文選題：互連網(wǎng)絡(luò) + 并行計(jì)算��； 參考：《中國(guó)科學(xué)技術(shù)大學(xué)》2013年博士論文

【摘要】：互連網(wǎng)絡(luò)在并行計(jì)算和通信系統(tǒng)中發(fā)揮著重要作用.網(wǎng)絡(luò)的容錯(cuò)性是評(píng)價(jià)互連網(wǎng)絡(luò)性能的關(guān)鍵指標(biāo),它主要考慮在網(wǎng)絡(luò)發(fā)生故障的時(shí)候網(wǎng)絡(luò)中某些特有性質(zhì)的保持能力.本文主要以圖論作為工具研究故障出現(xiàn)時(shí)網(wǎng)絡(luò)保持三種性質(zhì)的能力：多對(duì)多不交長(zhǎng)路存在性,連通分支最小度,連通分支子網(wǎng)絡(luò)結(jié)構(gòu).在研究中,本文利用高對(duì)稱網(wǎng)絡(luò)在不同維度上分解的等價(jià)性,探索出一套分析網(wǎng)絡(luò)容錯(cuò)性的有效方法,解決了幾個(gè)懸而未決的問(wèn)題. 本文第一章介紹所考慮問(wèn)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(diǎn)故障超立方體Qn中的k條多對(duì)多不交路問(wèn)題.在考慮條件容錯(cuò)的前提下,證明故障點(diǎn)數(shù).f不超過(guò)2n-2k-3時(shí),對(duì)于Qn中在不同部的兩個(gè)k-點(diǎn)集合S與T,存在至少含有2n-2f頂點(diǎn)的k條頂點(diǎn)不交的無(wú)故障路連接S與T.這個(gè)結(jié)果改進(jìn)了很多已知的結(jié)論. 本文的第三、四章主要分析類超立方體和星圖的容錯(cuò)性能.理論上講,類超立方體和星圖具備成為互連網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)的很好潛質(zhì),是超立方體的強(qiáng)有力的競(jìng)爭(zhēng)網(wǎng)絡(luò).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(duì)于點(diǎn)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(luò)的高階限制點(diǎn)(邊)連通度和高階嵌入限制點(diǎn)(邊)連通度,其中對(duì)星圖高階限制點(diǎn)連通度的確定證實(shí)了同行學(xué)者提出的猜想. 本文的第五、六章主要分析廣義星圖網(wǎng)絡(luò)和交換超立方體的高階限制連通性.廣義星圖網(wǎng)絡(luò)是星圖的網(wǎng)絡(luò)的推廣,它的變化更加靈活,受到了很多學(xué)者的關(guān)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(zhì),同時(shí)降低了連接復(fù)雜性.本文在第五、六章分別確定廣義星圖網(wǎng)絡(luò)和交換超立方體的高階限制點(diǎn)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(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：O157.5;TP302.8

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本文編號(hào)：1992585