交叉立方体中嵌入超立方体的研究

Efe提出的交叉立方体(crossedcube)是超立方体(hypercube)的一种变型。但是,交叉立方体的某些性质却优于超立方体,其直径几乎是超立方体的一半。在本文中,研究了用交叉立方体互连网络来模拟超立方体互连网络,其实质是图嵌入问题,得出了以下结论:当n≤2,2n维交叉立方体CQ2n可同构嵌入两个n 1维立方体Qn 1。当n≥3,2n维交叉立方体CQ2n可同胚嵌入n 1维超立方体Qn 1。     

交换超立方体网络的网络嵌入研究

本文主要研究超立方网和星型网嵌入交换超立方体网络的问题。首先,利用图形嵌入的方法,设计了超立方网到交换超立方体网络的嵌入映射,分析并证明了该嵌入映射所具有的评价性能。其次,给出了星型网到交换超立方体网络两种嵌入策略,也就是所谓的优化嵌入映射和奇偶嵌入映射,进而给出了具有更小的扩张率的星型网到另一种交换超立方体网络的嵌入方法。     

交换超立方网中的最短路径路由算法

针对交换超立方网络的最短路由问题,提出一个交换超立方网中的最短路径路由算法.利用图论的方法,通过引进子网的概念,研究交换超立方网的拓扑性质,给出节点各边可进行最短路径路由的充要条件,得到其时间复杂度为O(s+t)2).理论分析和仿真结果表明,该算法可输出交换超立方网中任意两节点间的一条最短路径.     

基于比较模型的交换超立方网络的(t,k)诊断度研究

故障诊断问题已经被广泛讨论,许多互连网络的诊断度已被深入研究。(t,k)-诊断为最重要的系统级故障诊断策略之一,在故障节点不大于t的前提条件下,每次迭代均可以识别最少故障节点个数为k。针对如何提高交换超立方网络的诊断度的问题,进行了一个基于比较模型的(t,k)-诊断算法研究,根据连通图的特性对交换超立方网络进行连通分子的划分,并计算交换超立方连通图中连接边与节点间的量化关系,从而证明了交换超立方网络是(t,k)-可诊断的。最终表明,本算法下的诊断度,优于其传统精确诊断s 1。     

3元◢n◣立方体网络的◢t/k◣可诊断度研究

可诊断度是评估多处理器系统可靠性的一个关键指标.t/k诊断策略通过允许至多k个无故障处理器被误诊为故障处理器,从而极大提高了系统的可诊断度.与t可诊断度和t1/t1可诊断度相比,t/k可诊断度可以更好地反映实际系统的故障模式.3元n立方是一种性质优良并且应用广泛的网络拓扑,在许多分布式多处理器的构建中被用做底层网络.根据一些引理以及确定系统为t/k可诊断的充分条件,研究得出当n≥3及0≤k≤n,3元n立方是tk,n/k-可诊断的,其中tk,n=2(k+1)n-(k+1)(k+2).这个结果显示,在选择恰当的k值时,3元n立方的t/k可诊断度tk,n远大于其t可诊断度2n和t1/t1可诊断度4n-3.     

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。     

交换交叉立方网络的g正确邻结点条件诊断度研究

系统级故障诊断是保障多处理器计算机系统运行可靠性的一种重要手段。为了提高系统的诊断能力,增强系统的可靠性,在条件诊断度的基础上Peng等人进一步提出了[g]正确邻结点条件诊断度,[g]正确邻结点条件诊断度是一种更加适用于大规模多处理器计算机系统的故障诊断方式。以新型互连网络拓扑结构研究的最新成果--交换交叉立方网络为研究对象,在得到交换交叉立方网络的[Rg]点连通度的基础上,首次证得交换交叉立方网络[(ECQ(s,t))]在PMC模型下的[g]正确邻结点条件诊断度为[2g(s+2－g)－1],其中[t≥s>g],进而通过模拟实验验证了结论的正确性和有效性。该研究对于理清交换交叉立方网络的可靠性能并有效推动交换交叉立方网络的应用和推广,有着非常重要的理论价值和现实意义。     

局部扭立方体网络中网络嵌入问题的研究

局部扭立方体网络LTQ_n(Locally Twisted Cube)作为超立方体网络Q_n(Hypercube)的优化变种网络,具有很多优良的特性。依据局部扭立方体网络的性质及图嵌入的理论提出二项树、交换超立方体网络和超立方体网络嵌入到局部扭立方体网络的方案,并严格证明了这几种嵌入映射的扩张率、拥塞度及负载等都是最小的,这说明了局部扭立方体网络具有很好的通用性。     

基于比较诊断模型的超立方网络诊断算法

一个有效的诊断算法对多处理器系统而言极其重要。在多处理器系统中,识别所有故障节点的能力称为诊断系统的诊断度。在比较模型下,诊断 的执行是通过一个比较器处理器,给与之相邻的一对处理器发送相同的输入信号,并比较两者间的响应状态。为了提高超立方网络的诊断度,提出了一种新型的基于比较模型的超立方故障诊断算法,其利用超立方网络节点连接的特性生成一个拓扑图ES(k;n),最终得出一个3位二进制的诊断症候集,从而确定系统故障节点。该算法的诊断度最优能达到4n,大于传统超立方的诊断度n。     

基于超立方体和圈的细胞分裂生长网络及其性质

立方连通圈是超立方体的有界变型,在这篇文章中作者以立方连通圈网络CCC(n)(n>2)为基础设计了一种新网络--CCC(n,k)(n>2且k是非负数),它是3正则3连通的,且有许多好的性质。作者证明了CCC(3,0)是哈密尔顿连通图,且CCC(n,k)(n>2且k是非负数)是哈密尔顿图,但当k>2和n>2或者k=1和22且k是非负数)和C_m的笛卡尔积的一些性质。     

Low expansion packings and embeddings of hypercubes into stargraphs: a performance-oriented approach

We discuss the problem of packing hypercubes into an n-dimensional star graph S(n), which consists of embedding a disjoint union of hypercubes U into S(n) with load one. Hypercubes in U have from [n/2] to (n+1)·[log₂ n]-2([lod₂n]+1)+2 dimensions, i.e., they can be as large as any hypercube which can be embedded with dilation at most four into S(n). We show that U can be embedded into S(n) with optimal expansion, which contrasts with the growing expansion ratios of previously known techniques. We employ several performance metrics to show that, with our techniques, a star graph can efficiently execute heterogeneous workloads containing hypercube, mesh, and star graph algorithms. The characterization of our packings includes some important metrics which have not been addressed by previous research (namely, average dilation, average congestion, and congestion). Our packings consistently produce small average congestion and average dilation, which indicates that the induced communication slowdown is also small. We consider several combinations of node mapping functions and routing algorithms in S(n), and obtain their corresponding performance metrics using either mathematical analysis or computer simulation     

Embedding of tree networks into hypercubes

The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube only with large expansion cost or large dilation cost.     

Optimal path embedding in crossed cubes

The crossed cube is an important variant of the hypercube. The n-dimensional crossed cube has only about half diameter, wide diameter, and fault diameter of those of the n-dimensional hypercube. Embeddings of trees, cycles, shortest paths, and Hamiltonian paths in crossed cubes have been studied in literature. Little work has been done on the embedding of paths except shortest paths, and Hamiltonian paths in crossed cubes. In this paper, we study optimal embedding of paths of different lengths between any two nodes in crossed cubes. We prove that paths of all lengths between [(n+1)/2] and 2/sup n/-1 can be embedded between any two distinct nodes with a dilation of 1 in the n-dimensional crossed cube. The embedding of paths is optimal in the sense that the dilation of the embedding is 1. We also prove that [(n+1)/2]+1 is the shortest possible length that can be embedded between arbitrary two distinct nodes with dilation 1 in the n-dimensional crossed cube.     

A Comment on "The Exchanged Hypercube'

We address and analyze the problems existing on the exchanged hypercube proposed by Loh et al., an interconnection network obtained by systematically removing links from a hypercube. By taking the wrong number of links, the exchanged hypercube suffers from two problems. Necessary modifications on the exchanged hypercube, including the incremental expandability and the ratio of the number of links in EH(s, t) to that of an (s+t+1)-dimensional hypercube, are made     

The embedding of rings and meshes into RP(k) networks

Copyright by Science in China Press 2004 Interconnection networks, as an important means in parallel processing systems, are investigated widely[1,2]. Recently a class of lower-degree networks is proposed[2—4]. In ref. [3] we have investigated a constant degree network, called RP(k) network. Com-pared with rings and 2-D mesh networks, the RP(k) network has many good properties. The RP(k) network has a much smaller diameter than that of 2-D meshes when the number of network nodes is less …     

Embedding multi-dimensional meshes into twisted cubes

The twisted cube is an important variant of the most popular hypercube network for parallel processing. In this paper, we consider the problem of embedding multi-dimensional meshes into twisted cubes in a systematic way. We present a recursive method for embedding a family of disjoint multi-dimensional meshes into a twisted cube with dilation 1 and expansion 1. We also prove that a single multi-dimensional mesh can be embedded into a twisted cube with dilation 2 and expansion 1. Our work extends some previously known results.     

Embedding a family of meshes into twisted cubes

The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The twisted cube is an important variation of the hypercube. Let TQn denote the n-dimensional twisted cube. In this paper, we consider embedding a family of 2-dimensional meshes into a twisted cube. The main results obtained in this paper are: (1) For any odd integer n?1, there exists a mesh of size 2ײn−1 that can be embedded in the TQn with unit dilation and unit expansion. (2) For any odd integer n?5, there exists a mesh of size 4ײn−2 that can be embedded in the TQn with dilation 2 and unit expansion. (3) For any odd integer n?5, a family of two disjoint meshes of size 4ײn−3 can be embedded into the TQn with unit dilation and unit expansion. Results (1) and (3) are optimal in the sense that the dilations and expansions of the embeddings are unit values.     

Improved compressions of cube-connected cycles networks

We present a new technique for the embedding of large cube-connected cycles networks (CCC) into smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a fixed size. Using the new embedding strategy, we show that the CCC of dimension I can be embedded into the CCC of dimension k with dilation 1 and optimum load for any k, l∈ N, k⩾8, such 5/3+c_k<1/k⩽2, c_k=3.2(2/3k)/4k+3, thus improving known results. Our embedding technique also leads to improved dilation-1 embeddings in the case 3/2<1/k⩽5/3+C_k     

On Embedding Binary Trees into Hypercubes

Hypercubes are known to be able to simulate other structures such as grids and binary trees. It has been shown that an arbitrary binary tree can be embedded into a hypercube with constant expansion and constant dilation. This paper presents a simple linear-time heuristic which embeds an arbitrary binary tree into a hypercube with expansion 1 and average dilation no more than 2. We also give some results extending good embeddings for parity-balanced binary trees to arbitrary binary trees. In particular, we show that a conjecture of I. Havel (Časopis Pěest. Mat.109 (1984), 135-152) implies embeddings of binary trees into hypercubes with expansion 1 and either dilation 2 or average dilation approaching 1, and embeddings with expansion 2 and dilation 1.