3元n立方网络的2阶超连通性

为了度量以3元n立方网络为底层拓扑结构的并行与分布式系统的连通性,通过构造其2阶超割的方法,计算出当n不小于2时,3元n立方网络的2阶超连通度是6n-7。证明了对于以3元n立方网络为底层拓扑结构的并行与分布式计算机系统,当有不超过6n-8个节点发生故障且每个连通分支至少还有3个健康的节点时,该并行与分布式系统的任意两个节点之间仍然有一条无故障的通信线路。     

超级Mbius立方体──一类最优容错的小直径互连网络

文中将具有２ｎ个顶点的Ｍｏｂｉｕｓ立方体的拓扑结构加以改变,得到了包含任意个顶点的互连网络——超级Ｍｏｂｉｕｓ立方体,并证明它保持了Ｍｏｂｉｕｓ立方体的高连通度、对数级的直径和顶点度数等优良性质,并且当顶点个数Ｎ＝２ｎ＋２ｎ－１时,０－型超级Ｍｏｂｉｕｓ立方体是一个（ｎ＋１）－正则图;更进一步地,由于它包含任意个顶点,所以其升级只需增加任意个顶点,从而克服了Ｍｏｂｉｕｓ立方体的升级必须成倍增加其顶点个数的缺点．     

Fault-free mutually independent Hamiltonian cycles of faulty star graphs

The star graph interconnection network has been recognized as an attractive alternative to the hypercube for its nice topological properties. Unlike previous research concerning the issue of embedding exactly one Hamiltonian cycle into an injured star network, this paper addresses the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty star network. To be precise, let SG _n denote an n-dimensional star network in which f≤n?3 edges may fail accidentally. We show that there exist (n?2?f)-mutually independent Hamiltonian cycles rooted at any vertex in SG _n if n∈{3, 4}, and there exist (n?1?f)-mutually independent Hamiltonian cycles rooted at any vertex in SG _n if n≥5.     

论PANCAKE互连网的连通性

本详细地讨论了ｎ－Ｐａｎｃａｋｅ在栅去不超过２ｎ－４个结点时的连通情况，并由此给出ｎ－Ｐａｎｃａｋｅ的条件连通度和条件直径，从本可以看出，ｎ－Ｐａｎｃａｋｅ是一种具有很强连通性的较好的并行网络拓扑结构。     

自适应路由算法优于确定性路由算法

在研究并行计算机系统的容错时。自适应路由算法是一个极为重要的研究课题．它是在网络结点出错时,算法通过可选择的路径进行路由．在每个结点具有独立的出错概率的模型下,研究Mesh网络上自适应路由算法和确定性路算法的性能．本文提出的技术使得我们能严格地推导出路由算法的成功的概率,从而能分析和比较算法的性能．研究结果表明自适应路由算法具有明显的优势：一方面确定性路算法需要全局错误信息而变得高效性,另一方面自适应路由算法对于结点出错和网络规模具有更好的健壮性而具有更高的成功概率．     

基于结点出错概率的Mesh网络容错性分析

在并行计算机系统中,Mesh网络是最重要的网络拓扑结构之一。该文研究了基于结点出错概率Mesh网络的连通性,提出了k-Mesh子网连通的概念,运用严格的数学推理,推导出网络结点出错概率和Mesh网络的连通概率之间的关系。研究表明:特定的Mesh网络能保持相当高的连通概率,例如,笔者严格证明了,当网络结点出错概率控制在0.1%以下,则对多达几十万个结点的Mesh网络,网络连通的概率仍可保持在99%以上。     

A Kind of Multistage Interconnection Networks with Multiple Paths

1ThisworkwassupportedbytheNationalNaturalScienceFoundationofChina,GralltNo.69473024.1IntroductionMultiprocessorsystemsoftenuseinterconnectionnetworkstoconnectproces-sorsormemorymodules-Atime-sharedbusisthesimplestformofinterconnectionnetworks,butitcannotprovidetheperformancerequiredinmultiprocessorsystemstoday.Acrossbarswitchnetworkisanalternativeusedintheearliersystemstoimplementinterconnection.Theonlydelaytoconnectinputstooutputsisthatofasingleswitchinggate,butacrossbarswitchnetworkisver…     

点对点网络容错路由算法的概率分析

基于网络中结点错误概率 ,提出一种新的概率分析方法 ,对网络中点对点的路由算法的容错性概率、路径长度、算法复杂性进行严格的推导 .以超立方体网络为分析的网络拓扑 ,提出在其上的一个路由算法 .分析表明 :在所有实际规模的超立方体网络中 (其结点数可以高达十亿个 ) ,在相当大的结点出错概率 (可高达 8% )的情况下 ,路由算法可达到 99.9%的成功概率     

三维直角坐标系下三环网络的超L型瓦仿真

传统的超L型瓦仿真算法主要采用穷举的方法,效率较低,且有一定的局限性。针对上述问题,将三维直角坐标系引入三环网络,在三维直角坐标系下,提出广义三环网络G(N;s1,s2,s3)的超L型瓦仿真算法,利用C++和OpenGL实现超L型仿真,并求得其相关参数l、m、n,以及三环网络的直径D。实验结果表明,该算法具有较高的执行效率和更强的通用性。     

具有大量错误结点的超立方体网络中的单播路由算法的设计与分析

本文讨论具有大量错误结点的超立方体网络中的单播路由算法，假定Hn是一个局部3－维子立方体连通的n-维超立方体网络并且每一个基本的3－维子立方体中分别最多有1个和2个错误结点，本文提出的单播路由算法能够在线性时间找到路径长度分别为源结点和目的结点之间大约1．5倍和2倍海明距离的次优路径，我们提出的单播路由算法只需要结点知道其邻结点的状态，而无需知道整个网络信息，也就是说，该算法是基于局部信息的，因而该算法具有很强的实际意义。     

Graph theoretic characterization and reliability of the generalized Boolean n-cube network

In this paper, a general class of Boolean n-cube structures is investigated. The interconnection is based on a mixed radix number system which results in a variety of generalized Boolean n-cube structures for a given number of processors , where x and y are positive integers. A number of interesting properties of the network are revealed. By a constructive method, the node connectivity of this network is found. Finally, we show that the graph is super-λ and is an optimal reliable structure for interconnection networks.     

Biswapped networks: a family of interconnection architectures with advantages over swapped or OTIS networks

We propose a new family of communication architectures called ‘biswapped networks’. Given any n-node basis network Ω, the associated biswapped network Bsw(Ω) is built of 2n copies of Ω, using a simple rule for connectivity that ensures desirable attributes, including regularity, modularity, fault tolerance, and algorithmic efficiency. In particular, if Ω is a Cayley digraph, then so is Bsw(Ω). Our biswapped connectivity provides a systematic scheme for synthesizing large, scalable, modular, and robust parallel architectures. Furthermore, many desirable attributes of the underlying basis network Ω are preserved, as the Bsw(Ω) parameters are related to the corresponding parameters of Ω. We obtain a number of results on internode distances, Hamiltonian cycles, optimal routing, and node-disjoint paths for Bsw(Ω). We explore the relations between biswapped and swapped or optical transpose interconnection system (OTIS) networks, which may use a mix of electronic and optical links. In particular, we demonstrate that the biswapped connectivity removes an inherent asymmetry of swapped/OTIS networks, as well as the attendant complications in analyses and applications. Finally, we show that biswapped networks are complementary to, and offer advantages over, well-known and widely used interconnection architectures for parallel processing.     

超立方体网络的3路结构连通度及子结构连通度

针对以超立方体网络为蓝本的多处理机系统的可靠性和容错能力的精准度量问题,结合多处理机系统遭受计算机病毒攻击时常常发生结构性故障的特点,研究了n维超立方体网络的结构连通性和子结构连通性评价问题。首先,使用构造n维超立方体网络的3路结构割的方法得到其3路结构连通度的一个上界;然后,使用构造n维超立方体网络的3路子结构集的等价变换或约简变换的方法,得到其3路结构子连通度的一个下界;最后,利用任意网络的3路结构连通度不小于3路子结构连通度的性质,证实了超立方体网络的3路结构连通度和子结构连通度均为该超立方体网络维数的一半。这一结果表明,在3路结构故障模型下,破坏敌方以超立方体网络为底层拓扑的多处理系统至少需要攻击该系统中维数一半的3路结构或子结构。     

Biswapped网络(BSN)的拓扑性质研究:点对称性和极大容错性

Biswapped网络(BSN)是一类两层结构的互连网络,它以任意图为模块且模块间采用一种完全两部图方式互连.BSN的互连形式与OTIS网络(即Swapped网络)类似但互连规则更一致,使得BSN展现出更好的性能.文中主要研究BSN的点传递性和容错性能.首先证明BSN能继承因子网络的点传递性质,为BSN上的分析和算法简单性找到理论依据.其次,通过直接构造网络中两点间最大数目的点不相交路径证明以任意连通图为因子网络的BSN是一致极大容错的.这些结果表明BSN既能继承因子网络的理想性能还展现某些好的新特性.最后,通过与OTIS网络、卡式积网络等层次类网络比较表明,BSN提供了一种构建可扩展性、模块化、容错性的大规模并行计算机系统的潜在有竞争力的体系结构形式.     

Super connectivity of Kronecker products of graphs

Let G₁ and G₂ be two connected graphs. The Kronecker product G₁×G₂ has vertex set V(G₁×G₂)=V(G₁)×V(G₂) and the edge set . In this paper, we show that if G is a bipartite graph with κ(G)=δ(G), then G×Kn(n?3) is super-κ.