Finding the roots of a polynomial on an MIMD multicomputer

This paper introduces the parallelization on a distributed memory multicomputer of two iterative methods for finding all the roots of a given polynomial. The parallel algorithms share the computation of the roots among the processors and perform a total exchange of the data at each step. Since the amount of communications is the main drawback of this approach, we study the effect of the network topology on the performance of the algorithms. Particularly, we show that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications. For each topology is computed the optimal number of processors. Experiments on the hypercube FPS T40 illustrate the results.     

Efficient Collective Communications in Dual-Cube

The hypercube, or n-cube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network, namely dual-cube, for large-scale parallel computers and describes the algorithms for efficient collective communications in dual-cube. The dual-cube network mitigates the problem of increasing number of links in the large-scale hypercube network while retains hypercube's topological properties. Design of efficient routing algorithms for collective communications is the key issue for any interconnection network. In this paper, we show that the collective communications can be done in dual-cube with almost the same communication times as in hypercube.     

A spanning multichannel linked hypercube: a gradually scalableoptical interconnection network for massively parallel computing

A new, scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed. This proposed network is very suitable to massively parallel systems and is highly amenable to optical implementation. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multichannel links (similar to spanning buses). In doing so, the SMLH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SMLH topology supports many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SMLH network is its ability to support a large number of processors with the possibility of maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. It is shown that the SMLH network provides better average message distance, average traffic density, and queuing delay than many similar networks, including the binary hypercube, the SBH, etc. Additionally, the SMLH has comparable performance to other high-performance hypercubic networks, including the Generalized Hypercube and the Hypermesh. An optical implementation methodology is proposed for SMLH. The implementation methodology combines both the advantages of free space optics with those of wavelength division multiplexing techniques. A detailed analysis of the feasibility of the proposed network is also presented     

平衡超立方体的故障容错性

故障容错是衡量多处理器互连网络可靠性的重要方式之一。其中g-限制边连通度和g-限制连通度保证了剩下每个分支之间不连通且每个分支中节点的邻居数目不少于 g,能够更加精准地测量多处理器和多信道系统的容错性和可靠性。平衡超立方体是超立方体的一个变形,它特有的良好拓扑性质能够更好地满足多处理器系统和多种新型网络的需要。提出了n维平衡超立方体的{1,2}-限制边连通度和{1,2}-限制连通度,能够丰富以平衡超立方体为拓扑结构的网络容错性和可靠性的评价体系,并为平衡超立方体的故障诊断算法打下良好基础。     

Hierarchical Hypercube Networks (HHN) for Massively Parallel Computers

The hypercube is one of the most widely used topologies because it provides small diameter and embedding of various interconnection networks. For very large systems, however, the number of links needed with the hypercube may become prohibitively large. In this paper, we propose a hierarchical interconnection network based on hypercubes called hierarchical hypercube network (HHN) for massively parallel computers. The HHN has a smaller number of links than the comparable hypercube and in particular, when we construct networks with 2^Knodes, the node degree of HHN with the minimum node degree isO([formula]) while that of hypercube isO(K). Regardless of its smaller node degree, many parallel algorithms can be executed in HHN with the same time complexity as in the hypercube.     

Adaptive routing in wormhole-switched necklace-cubes: Analytical modelling and performance comparison

The necklace hypercube has recently been introduced as an attractive alternative to the well-known hypercube. Previous research on this network topology has mainly focused on topological properties, VLSI and algorithmic aspects of this network. Several analytical models have been proposed in the literature for different interconnection networks, as the most cost-effective tools to evaluate the performance merits of such systems. This paper proposes an analytical performance model to predict message latency in wormhole-switched necklace hypercube interconnection networks with fully adaptive routing. The analysis focuses on a fully adaptive routing algorithm which has been shown to be the most effective for necklace hypercube networks. The results obtained from simulation experiments confirm that the proposed model exhibits a good accuracy under different operating conditions.     

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     

Mesh-connected trees: a bridge between grids and meshes of trees

The grid and the mesh of trees (or MOT) are among the best-known parallel architectures in the literature. Both of them enjoy efficient VLSI layouts, simplicity of topology, and a large number of parallel algorithms that can efficiently execute on them. One drawback of these architectures is that algorithms that perform best on one of them do not perform very well on the other. Thus there is a gap between the algorithmic capabilities of these two architectures. We propose a new class of parallel architectures, called the mesh-connected trees (or MCT) that can execute grid algorithms as efficiently as the grid, and MOT algorithms as efficiently as the MOT, up to a constant amount of slowdown. In particular, the MCT topology contains the MOT as a subgraph and emulates the grid via embedding with dilation 3 and congestion two. This significant amount of computational versatility offered by the MCT comes at no additional VLSI area cost over these earlier networks. Many topological, routing, and embedding properties analyzed here suggest that the MCT architecture is also a serious competitor for the hypercube. In fact, while the MCT is much simpler and cheaper than the hypercube, for all the algorithms we developed, the running time complexity on the MCT matches those of well known hypercube algorithms. We also present an interesting variant of the MCT architecture that admits both the MOT and the torus as its subgraphs. While most of the discussion in this paper is focused on the MCT architecture itself, these analyses can be easily extended to the variant of the MCT presented here     

Embedding hierarchical hypercube networks into the hypercube

The embedding of one interconnection network into another is a very important issue in the design and analysis of parallel algorithms. Through such embeddings, the algorithms originally developed for one architecture can be directly mapped to another architecture. This paper describes a new embedding method, based on matrix transformations, for optimally embedding hierarchical hypercube networks (HHNs) into the hypercube (binary n-cube). Thus, this embedding method has practical importance in enhancing the capabilities and extending the usefulness of the hypercube, since hierarchical hypercube networks have proven to be very cost-effective for a wide range of applications     

基于多层立方体簇结构的3D-Ad hoc网络路由算法

针对三维Ad hoc网络拓扑结构复杂和节点随机移动导致寻路困难的问题,提出了基于多层立方体簇结构的路由算法。借助节点的位置信息构建多层立方体,成簇过程简便并且扩展性强;由于节点随机移动,引入了簇重构机制。利用多层立方体簇进行拓扑转化及簇间通信编号。簇间通信编号能够提供到达地址的相关路径信息,有效简化了路由过程。仿真分析表明,提出的策略正确可行,达到了简化三维Ad hoc网络拓扑、正确路由的目的。     

一种高斯-马尔科夫模型下的车辆位置管理策略

在车载自组网VANET中,节点的高移动性使得网络的拓扑结构频繁变化。随着节点数目的增加,网络的开销迅速增大,直接影响到网络的可扩展性。为此,将位置管理的策略引入VANET网络中,以达到减少网络开销的目的。在高斯-马尔科夫移动模型的基础下,提出了一种新的位置管理策略,实现车辆在低开销下的可靠通信。通过仿真比较,验证其在性能上具有更好的可扩展性。     

一种引入阈值的Ad Hoc网络分级转发指针的位置管理策略

在移动Ad Hoc网络中,由于网络具有自组织性和节点的频繁移动,也就使得网络的拓扑结构频繁变化。随着节点数目的增加,网络的开销迅速增大,这就直接影响到网络的可扩展性。目前,在移动Ad Hoc网络中越来越多的引入了位置管理的策略,以达到减少网络开销的目的。引入分级转发指针和阈值的思想,提出了一种新的位置管理策略。通过与其他策略的方针比较,证明其在性能上具有更好的可扩展性。     

LHL-立方体互连网络及其性质

并行计算系统一直是计算机科学中的重要研究领域,其互连网络的拓扑性质对整个网络的性能起着非常重要的作用.目前已经提出多种互连网络,其中超立方体具有对数级的直径、高连通度、对称性等很好的性质,故被用作多种并行机的处理器连接的拓扑结构.然而,超立方体并非所有性质都是最优的互连网络,且超立方体的许多变型结构具有许多比超立方体更好的性质,其中已经证明了局部扭立方体在直径、Hamilton连通性等方面都优于超立方体.给出在超立方体与局部扭立方体的顶点间的一种连接方式--超连接,从而得到一种称为LHL-立方体的新型网络,并对这种网络的以下性质进行了研究:顶点连通度、边连通度、Hamilton连通性、直径.研究结果表明,一个n维LHL-立方体是一个具有2n个顶点和n2n-1条边的n-正则图,n维LHL-立方体的顶点连通度和边连通度均为n,且是Hamilton连通的,直径上界为[n/2 ]+3.     

On a class of recursive network topologies

For the interconnection of the nodes of massively parallel processor networks, concepts are required, which are extendable. In this paper, a ‘recursive network’ is described. With a basic building block, essentially with a fixed number of links, arbitrarily large systems can be configured. At all levels, the interconnection topology is the same. Hence, a simple routing algorithm can be applied. The recursive network is described and compared with hypercube and mesh networks (with respect to the system diameter and the efficient use of the links).     

Executing algorithms with hypercube topology on torusmulticomputers

Many parallel algorithms use hypercubes as the communication topology among their processes. When such algorithms are executed on hypercube multicomputers the communication cost is kept minimum since processes can be allocated to processors in such a way that only communication between neighbor processors is required. However, the scalability of hypercube multicomputers is constrained by the fact that the interconnection cost-per-node increases with the total number of nodes. From scalability point of view, meshes and toruses are more interesting classes of interconnection topologies. This paper focuses on the execution of algorithms with hypercube communication topology on multicomputers with mesh or torus interconnection topologies. The proposed approach is based on looking at different embeddings of hypercube graphs onto mesh or torus graphs. The paper concentrates on toruses since an already known embedding, which is called standard embedding, is optimal for meshes. In this paper, an embedding of hypercubes onto toruses of any given dimension is proposed. This novel embedding is called xor embedding. The paper presents a set of performance figures for both the standard and the xor embeddings and shows that the latter outperforms the former for any torus. In addition, it is proven that for a one-dimensional torus (a ring) the xor embedding is optimal in the sense that it minimizes the execution time of a class of parallel algorithms with hypercube topology. This class of algorithms is frequently found in real applications, such as FFT and some class of sorting algorithms     

Construction of a large-scale neural network: Simulation of handwritten Japanese character recognition on NCUBE

This paper describes how new learning methods may make it possible for a large-scale, hierarchical neural network to recognize most Japanese handwritten characters. This is a very large and complex task, as the Japanese character set consists of about 3000 categories which can be written in many different ways. Such a difficult task can lead a neural network to converge very slowly and to yield recognition rates that are uneven between categories. To address these problems we here propose five learning methods as modifications of the conventional back-propagation learning rule. These methods produce fast convergence, even recognition rates over all categories, and adequate recognition of test samples. We also describe how a large-scale neural network can be built by dividing the recognition task into several subtasks, with networks for each subtask, and then integrating these subnetworks in a large network with a hierarchical structure. In a hierarchical network, the upper level network directly integrates outputs from each lower level network. Application of that network to handwritten Japanese character recognition has resulted in poor recognition, because lower level networks do not know about unknown input patterns, and the direct integration of ambiguous outputs from many lower level networks confuses the upper level network. We propose a new integration method which provides each subnetwork with more information as to how close an input pattern is to the categories of that subnetwork. This method resulted in high recognition performance for character recognition. We here described the above methods, and report the performance of our implementation of a neural network for the recognition of 71 Hiragana characters, and describe our implementation of this network on a hypercube concurrent computer.     

dBCube: a new class of hierarchical multiprocessor interconnectionnetworks with area efficient layout

Introduces a class of hierarchical networks that is suitable for implementation of large multi-computers in VLSI with wafer scale integration (VLSI/WSI) technology. These networks, which are termed dBCube, employ the hypercube topology as a basic cluster, connect many of these clusters using a de Bruijn graph, and maintain the node connectivity to be the same for all nodes product graph. The size of this class of regular networks can be easily extended by increments of a cluster size. Local communication, to be satisfied by the hypercube topology, allows easy embedding of existing parallel algorithms, while the de Bruijn graph, which was chosen for JPL's 8096-node multiprocessor, provides the shortest distance between clusters running different parts of an application. A scheme for obtaining WSI layout is introduced and used to estimate the number of tracks needed and the required area of the wafer. The exact number of tracks in the hypercube and an approximation for the de Bruijn graph are also obtained. Tradeoffs of area versus static parameters and the size of the hypercube versus that of the de Bruijn graph are also discussed     

平均度约束的无线传感器网络拓扑控制

拓扑控制是无线传感器网络中最重要的技术之一.大规模随机部署的无线传感器网络节点,在满足无线传感器网络拓扑连通性的前提下,如何保证网络结构的稀疏性是一个亟待解决的问题,目前已有的研究结果表明当节点密度较大时,得到的网络拓扑复杂,计算路由将严重消耗节点资源.文中提出了一种平均度约束的无线传感器网络拓扑控制,通过增加节点通信半径,约束节点的平均度来解决网络的连通性与网络拓扑的稀疏性之间的矛盾.数值模拟表明:通过平均度约束的无线传感器网络拓扑控制,可减少网络中选出的工作节点数,保证了网络的稀疏性,简化了路由的复杂度,从而延长了网络的生存周期.     

Dynamic broadcasting in parallel computing

We consider the problem where broadcast requests are dynamically generated at random time instants at each node of a multiprocessor network. In particular, in our model packets arrive at each node of a network according to a Poisson process, and each packet has to be broadcast to all the other nodes. We propose an on-line, distributed routing scheme to execute the broadcasts in this dynamic environment. Our scheme consists of repeated execution of a partial multinode broadcast task, which is a static communication task where any M⩽N arbitrary nodes of an N-processor network broadcast a packet to all the other nodes. The dynamic broadcasting scheme that we propose can be used in any topology, regular or not, for which partial multinode broadcast algorithms with certain properties can be found. We derive such an algorithm and we analyze the corresponding dynamic broadcasting scheme for the hypercube network. We show that its stability region tends to the maximum possible as the number of nodes of the hypercube tends to infinity. Furthermore, for any fixed load in the stability region, the average delay is of the order of the diameter of the hypercube. Our analysis does not use any approximating assumptions     

A regular scalable fault tolerant interconnection network for distributed processing

Bounded degree networks like deBruijn graphs or wrapped butterfly networks are very important from VLSI implementation point of view as well as for applications where the computing nodes in the interconnection networks can have only a fixed number of I/O ports. One basic drawback of these networks is that they cannot provide a desired level of fault tolerance because of the bounded degree of the nodes. On the other hand, networks like hypercube (where degree of a node grows with the size of a network) can provide the desired fault tolerance but the design of a node becomes problematic for large networks. In their attempt to combine the best of the both worlds, authors in [IEEE Transactions on Parallel and Distributed Systems 4(9) (1993) 962] proposed hyper-deBruijn (HD) networks that have many additional features of logarithmic diameter, partitionability, embedding, etc. But, HD networks are not regular, are not optimally fault tolerant and the optimal routing is relatively complex. Our purpose in the present paper is to extend the concepts used in the above-mentioned reference to propose a new family of scalable network graphs that retain all the good features of HD networks and at the same time are regular and maximally fault tolerant; the optimal point to point routing algorithm is significantly simpler than that of the HD networks. We have developed some new interesting results on wrapped butterfly networks in the process.