Adaptive deadlock- and livelock-free routing with all minimal pathsin torus networks

This paper consists of two parts. In the first part, two new algorithms for deadlock- and livelock-free wormhole routing in the torus network are presented. The first algorithm, called Channels, is for the n-dimensional torus network. This technique is fully-adaptive minimal, that is, all paths with a minimal number of hops from source to destination are available for routing, and needs only five virtual channels per bidirectional link, the lowest channel requirement known in the literature for fully-adaptive minimal worm-hole routing. In addition, this result also yields the lowest buffer requirement known in the literature for packet-switched fully-adaptive minimal routing. The second algorithm, called 4-Classes, is for the bidimensional torus network. This technique is fully-adaptive minimal and requires only eight virtual channels per bidirectional link. Also, it allows for a highly parallel implementation of its associated routing node. In the second part of this paper, four worm-hole routing techniques for the two-dimensional torus are experimentally evaluated using a dynamic message injection model and different traffic patterns and message lengths     

A framework for designing deadlock-free wormhole routing algorithms

This paper presents a framework to design fully-adaptive, deadlock-free wormhole algorithms for a variety of network topologies. The main theoretical contributions are: (a) design of new wormhole algorithms using store-and-forward algorithms, (b) a sufficient condition for deadlock free routing by the wormhole algorithms so designed, and (c) a sufficient condition for deadlock free routing by these wormhole algorithms with centralized flit buffers shared among multiple channels. To illustrate the theory, several wormhole algorithms based on store-and-forward hop schemes are designed. The hop-based wormhole algorithms can be applied to a variety of networks including torus, mesh, de Brujin, and a class of Cayley networks, with the best known bounds on virtual channels for minimal routing on the last two classes of networks. An analysis of the resource requirements and performances of a proposed algorithm, called negative-hop algorithm, with some of the previously proposed algorithms for torus and mesh networks is presented     

基于InfiniBand的多链路mesh/torus大规模并行系统互连网络

在大规模并行系统中,系统级互连网络的设计至关重要.InfiniBand作为一种高性能交换式网络被广泛应用于大规模并行处理系统中.mesh/torus拓扑结构相较于目前普遍应用于InfiniBand网络的胖树拓扑结构拥有更好的性能与可扩展性.尽管如此,研究发现,用传统的mesh/torus拓扑结构构建InfiniBand互连网络存在诸多问题.分析了传统网络拓扑结构的缺陷,并提出了一种基于InfiniBand的多链路mesh/torus互连网络.这种改进型的拓扑结构通过充分利用交换机间的多链路可以获得比传统mesh/torus网络更高的带宽.另外,同时给出了与该网络拓扑结构相配套的高效路由算法.最后,通过网络仿真技术对提出的算法进行了评估,实验结果显示提出的路由算法相较于其他路由算法拥有更好的性能与可扩展性.     

A Generic Design Methodology for Deadlock-Free Routing in Multicomputer Networks

This paper introduces a generic methodology for defining deadlock-free wormhole routing schemes in any arbitrary network. The basic strategy is to partition a graph into subdigraphs with no cyclic dependencies and selectively assign virtual channels. The usefulness of our scheme is shown for the n-dimensional hypercube, the n-dimensional mesh, and the k-ary n-cube torus by identifying subdigraph characteristics that ensure acyclic routing. Further generalization which allows partial cyclic dependencies without deadlock is achieved by our extended generic methodology. We also illustrate how to identify shortest fixed path and nonminimal adaptive routing schemes using minimum required channels.     

Fully adaptive minimal deadlock-free packet routing in hypercubes,meshes, and other networks: algorithms and simulations

This paper deals with the problem of packet-switched routing in parallel machines. Several new routing algorithms for different interconnection networks are presented. While the new techniques apply to a wide variety of networks, routing algorithms will be shown for the hypercube, the two-dimensional mesh, and the shuffle-exchange. Although the new techniques are designed for packet routing, they can be used alternatively for virtual cut-through routing models. The techniques presented for hypercubes and meshes are fully-adaptive and minimal. A fully-adaptive and minimal routing is one in which all possible minimal paths between a source and a destination are of potential use at the time a message is injected into the network. Minimal paths followed by messages ultimately depend on the local congestion encountered in each node of the network. All of the new techniques are completely free of deadlock situations     

一个高效完全自适应路由器的设计

路由器在大规模并行处理机（MPP）系统中对互连网络通信性能和系统性能的发挥起着关键作用。根据全自适应路由算法BNP设计框架,给出Mesh上一类基于BNP的全自适应路由算法BBFAM（thBNR-based fully adaptive algorithms on mesh);同时提出并采用动态优先级流控,“自由度”通道选择策略,设计了一个基于BNR,简洁,低代价的高效完全自适应路由器BFR（the BNR-based fully adaptive router),并采用Aletera CPLD器件构造了原型系统。     

There is no optimal routing policy for the torus

A routing policy is the method used to select a specific output channel for a message from among a number of acceptable output channels. An optimal routing policy is a policy that maximizes the probability of a message reaching its destination without delays. Optimal routing policies have been proposed for several regular networks, including the mesh and the hypercube. An open problem in interconnection network research has been the identification of an optimal routing policy for the torus. In this paper, we show that there is no optimal routing policy for the torus. Our result is demonstrated by presenting a detailed example in which the best choice of output channel is dependent on the probability of each channel being available. This result settles, in the negative, a conjecture by Wu concerning an optimal routing policy for the torus.     

Constraint-based performance comparison of multi-dimensional interconnection networks with deterministic and adaptive routing strategies

Several studies have examined the relative performance merits of the torus and hypercube taking into account the channel bandwidth constraints imposed by implementation technology. While the torus has been shown to outperform the hypercube under the constant wiring density constraint, the opposite conclusion has been reached when the constant pin-out constraint is considered. However, all these studies have assumed deterministic routing and have not taken into account the internal hardware cost of routers. This paper re-examines the performance merits of the torus and hypercube using both fully-adaptive and deterministic routing strategies. Moreover, it uses a new cost model which takes into account the internal hardware cost of routers.     

Optimal Routing Based on Super Topology in Optical Parallel Interconnect

Traditionally the routing in optical parallel interconnect is based on an embedded virtual topology. However, one important fact that has been neglected in the past is that the wavelength assignment to transceivers actually creates additional (logical) links not present in the virtual topology. Such a side-effect can be utilized to significantly reduce the number of hops between a pair of processors. This observation leads to the concept of super topology. This paper considers the hypercube as the embedded virtual topology. The ideas contained here are easily applicable to optical parallel interconnects employing other virtual topologies as well. We present a general framework for embedding a regular topology, the structure of the super topology, the optimal routing algorithm, the distance between any pair of processors and the diameter in the super topology.     

YOMNA – An efficient deadlock-free multicast wormhole algorithm in 2-D mesh multicomputers

A mesh network is a popular architecture which has been implemented in many multicomputer systems. It is preferred because it offers useful edge connectivity and is partitioned into units that are still meshes. It is also scalable and has a number of features that make it particularly amenable to high-performance computing. The 2-D mesh topology has become increasingly important to multicomputer design because of its many desirable properties including scalability, low bandwidth and fixed degree of nodes.The essential pattern in new multicomputer generations is the multicast wormhole pattern, which corresponds to one-to-many communication in which one source sends the same message to multiple destination nodes. In wormhole routing, a message is decomposed into words or flits, and flits of one message may be spread out among several nodes. Deadlock in the interconnection network occurs when no message can advance towards its destination. Some deadlock-free routing algorithms for wormhole routing were proposed, but the network latency and the network traffic were not taken into consideration. An optimal message routing should achieve both minimum traffic and minimum latency for the communication patterns involved. Unfortunately, finding optimal message routing has been shown to be NP-hard for most common multicomputer topologies.In this paper, an efficient algorithm (YOMNA) is introduced to find a deadlock-free multicast wormhole routing in 2-D mesh parallel machines. YOMNA algorithm is a tree-based technique, in which the router simultaneously sends incoming flits on more than one outgoing channel. YOMNA algorithm is compared with the dual-path multicast routing, which is a path-based technique. YOMNA algorithm has proved to be deadlock free. The network latency and the network traffic are calculated for YOMNA algorithm and for the dual-path multicast routing. The results demonstrate that YOMNA algorithm outperformed the dual-path routing.     

The triangular pyramid: Routing and topological properties

In this paper, a new topology for multicomputer interconnection networks, based on triangular mesh, is proposed. The new network, referred to as the triangular pyramid (or tripy for short), has L levels of triangular mesh. We study some basic important properties of the proposed network as well as introduce a routing algorithm for the tripy network based on the routing of triangular meshes. We prove that this form of pyramidal network is Hamiltonian, Hamiltonian-connected, and pancyclic. We also prove that the proposed network is 6-colorable and conduct a brief comparison of the tripy and its traditional pyramid counterpart. Our results show that the proposed network has higher scalability, connectivity, and total network bandwidth while preserving the important properties of the traditional pyramid network.     

卫星路由算法研究

对目前几种主流的组网技术,包括异步传输模式(ATM),网际互连协议的协议栈(IP),多协议标签交换(MPLS),卫星网络与地面网络的网络构成、拓扑以及通信时延等特点作了分析比较,同时对地面网络上的主要的路由算法进行了分析,主要包括距离向量算法和链路状态算法等：给出了运行于卫星网络上的路由算法,并对路由算法的三种策略进行了分类分析,其中基于虚拟拓扑路由策略的路由算法多用于基于像ATM等面向连接的网络;而采用虚拟节点概念的路由算法常用于基于IP的路由;基于拓扑依赖策略的路由算法,对于特定的星座网络将会有较高的效率。     

Taking a free ride for routing topology inference in peer-to-peer networks

A Peer-to-Peer (P2P) network can boost its performance if peers are provided with underlying network-layer routing topology. The task of inferring the network-layer routing topology and link performance from an end host to a set of other hosts is termed as network tomography, and it normally requires host computers to send probing messages. We design a passive network tomography method that does not require any probing messages and takes a free ride over data flows in P2P networks. It infers routing topology based on end-to-end delay correlation estimation (DCE) without requiring any synchronization or cooperation from the intermediate routers. We implement and test our method in the real world Internet environment and achieved the accuracy of 92 % in topology recovery. We also perform extensive simulation in OMNeT++ to evaluate its performance over large scale networks, showing that its topology recovery accuracy is about 95 % for large networks.     

E-2D Torus网络结构中的无死锁路由算法

研究了太比特路由器核心交换网络拓扑的一种新结构-E-2Dtorus网络.该网络具有简单,对称,可扩展等优势.提出了适用于该网络结构的两种路由算法NPN(NoPositivetoNegative)和IDO(ImprovedDimensionOrder).部分自适应的NPN和确定性的IDO都是无死锁,无活锁且最短的路由算法.同时给出了无死锁无活锁的证明.最后,在8×8的E-2Dtorus网络上对路由算法进行仿真,结果表明E-2Dtorus是一种有潜力的网络拓扑结构,两种路由算法具有良好的性能.     

Honeycomb networks: Topological properties and communicationalgorithms

The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network. A honeycomb mesh network with n nodes has degree 3 and diameter ≈1.63√n-1, which is 25 percent smaller degree and 18.5 percent smaller diameter than the mesh-connected computer with approximately the same number of nodes. Vertex and edge symmetric honeycomb torus network is obtained by adding wraparound edges to the honeycomb mesh. The network cost, defined as the product of degree and diameter, is better for honeycomb networks than for the two other families based on square (mesh-connected computers and tori) and triangular (hexagonal meshes and tori) tessellations. A convenient addressing scheme for nodes is introduced which provides simple computation of shortest paths and the diameter. Simple and optimal (in the number of required communication steps) routing, broadcasting, and semigroup computation algorithms are developed. The average distance in honeycomb torus with n nodes is proved to be approximately 0.54√n. In addition to honeycomb meshes bounded by a regular hexagon, we consider also honeycomb networks with rhombus and rectangle as the bounding polygons     

On the performance of multicomputer interconnection networks

Several researchers have analysed the performance of k-ary n-cubes taking into account channel bandwidth constraints imposed by implementation technology, namely the constant wiring density and pin-out constraints for VLSI and multiple-chip technology respectively. For instance, Dally [IEEE Trans. Comput. 39(6) (1990) 775], Abraham [Issues in the architecture of direct interconnection networks schemes for multiprocessors, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1992], and Agrawal [IEEE Trans. Parallel Distributed Syst. 2(4) (1991) 398] have shown that low-dimensional k-ary n-cubes (known as tori) outperform their high-dimensional counterparts (known as hypercubes) under the constant wiring density constraint. However, Abraham and Agrawal have arrived at an opposite conclusion when they considered the constant pin-out constraint. Most of these analyses have assumed deterministic routing, where a message always uses the same network path between a given pair of nodes. More recent multicomputers have incorporated adaptive routing to improve performance. This paper re-examines the relative performance merits of the torus and hypercube in the context of adaptive routing. Our analysis reveals that the torus manages to exploit its wider channels under light traffic. As traffic increases, however, the hypercube can provide better performance than the torus. Our conclusion under the constant wiring density constraint is different from that of the works mentioned above because adaptive routing enables the hypercube to exploit its richer connectivity to reduce message blocking.     

Valiant load-balanced robust routing algorithm for multi-granularity connection requests in traffic-grooming WDM mesh networks

The paper considers the problem of establishing robust routes for multi-granularity connection requests in traffic-grooming WDM mesh networks and proposes a novel Valiant load-balanced robust routing scheme for the hose uncertain model. Our objective is to minimize the total network cost when construct the stable virtual topology that assure robust routing for all possible multi-granularity connection requests under the hose model. Since the optimization problem is shown to be NP-complete, two heuristic algorithms are proposed and evaluated. Finally we compare the traffic throughput of the virtual topology by Valiant load-balanced robust routing scheme with that of the traditional traffic-grooming algorithm under the same total network cost by computer simulation.     

Three-dimensional Petersen-torus network: a fixed-degree network for massively parallel computers

A two-dimensional (2D) Petersen-torus network is a mesh-class fixed-degree network designed using a Petersen graph, which has a maximum of 10 nodes when the degree is 3 and the diameter is 2 in a (d,k)-graph problem. Here, I propose a new three-dimensional (3D) Petersen-torus network that extends the 2D Petersen-torus network without increasing the degree. The 3D Petersen-torus has the same number of nodes (N). The 3D Petersen-torus is better than the well-known 3D torus and 3D honeycomb mesh in terms of diameter and network cost. The 3D Petersen-torus network is better than the hypercube-like and star graph-like networks in terms of extendibility. Hence, the proposed network may serve as the foundation for realizing a high-performance multicomputer. In this paper, the optimal routing algorithm, Hamilton cycle, and several basic attributes are discussed. Furthermore, a comparison with a mesh-class fixed-degree 3D network is made for degree, diameter, and network cost.     

基于局部故障块三维mesh/torus网的容错路由

当系统包含很少的故障点时．mesh/torus网整个系统就有可能是不可靠的．该文采用扩展的局部可靠性信息来指导三维mesh／torus网的容错路由．扩展的局部可靠性信息在每个平面内部对无故障节点分类，所以系统中的故障块也是在不同的平面上构成的，而不是基于整个系统．很多基于整个系统不可靠的节点在二维的平面中都会变成可靠的节点．不管是在可靠的系统内，甚或不可靠的系统内，扩展的局部可靠性信息都能有效地指导容错路由．不同于以往的方法，作者的方法不会将任何无故障节点设置为无效节点．所有的故障块都是在平面内构成的，而不是基于整个系统；在一个平面内．任何包含在故障块里的无故障节点仍然可作为出发点或者目标点，这样将大大提高系统的计算能力和性能．模拟结果表明该文方法大大优于已有的方法．     

直线引导的Torus结构路由算法

为了提高片上网络在Torus拓扑结构下的路由通信效率,提出了一种基于直线引导思想的路由算法Tline。该路由算法将Torus拓扑结构的片上网络拓展为类似Mesh结构的坐标平面,以数据包的源节点和目的节点构成的直线为路由转发方向,并根据周围邻近节点的拥塞状况选择传输路径方向实现部分自适应路由。实验结果表明,与XY、OE路由算法相比,在热点流量模式下Tline路由算法具有较好的路由性能,且平均能耗降低约8%。