蜂窝网络上的路由算法*

主要研究蜂窝网络上的无死锁单播路由算法和一对全的广播路由算法。基于蜂窝网络的砖形画法,利用二维网络维序路由的基本思想和两个虚拟网络实现了无死锁的最短单播路由算法,并证明了算法的无死锁性。然后基于这个单播路由算法和线列上的广播算法,用软件实现了蜂窝网络上一对全的广播路由算法,经过简单比较得出该广播算法比以往的算法在通信效率上有了极大的提高。     

双层二维网格结构间的Wormhole路由算法

二维网格结构由于其较好的可扩 展性而被越来越广泛地应用,因此对于二维网格结构多处理机间的数据通信,寻找一个好的路由算法也越来越重要。以Intel公司的Option Red机器为背景,分析了双层二维网格结构多处理机间的通信机制,并且针对该实际结构,根据单层二维网格结构中以Wormhole原理为基础的Unicast自适应路由算法,提出了适用于双层二维网格结构的无死锁的Wormhole路由算法。根据该算法得出的数据传输路径是无死锁的最短传输路径。     

双层二维网格结构间的Wromhole路由算法

二维网格结构由于其较好的可扩展性而被越来越广泛地应用，因此对于二维网格结构多处理机间的数据通信，寻找一个好的路由算法也越来越重要。以Intel公司的Option Red机器为背景，分析了双层二维网格结构多处理机间的通信机制，并且针对该实际结构，根据单层二维网格结构中以Wormhole原理为基础的Unicast自适应路由算法，提出了适用于双层二维网格结构的无死锁的Wormhole路由算法。根据该算法得出的数据传输路径是无死锁的最短传输路径。     

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.     

交叉立方体网络的无死锁虫洞路由算法

Efe提出的交叉立方体(crossed cube)是超立方体(hypercube)的一种变型.交叉立方体的某些性质优于超立方体,比如其直径几乎是超立方体的一半.首先证明n(n≥3)维交叉立方体网络不存在无死锁的最短路径路由算法,然后利用虚通道技术将一条物理通道分成三条逻辑通道,并在此基础上提出一种基于虫洞路由的最短路径路由算法,其时间复杂度为O(n).理论证明了算法是无死锁的.     

基于2D Mesh的NoC路由算法设计与仿真

在研究Turn Model模型的基础上,提出一种基于2D Mesh结构的XY-YX路由算法,是一种确定性的无死锁的最短路径路由算法。给出无死锁的证明,通过片上网络（NoC）模拟仿真实验平台NIRGAM,将该算法在一个4×4的2D Mesh网络中进行仿真,并与XY路由算     

一种邻节点状态感知的NoC可重构容错路由

芯片特征尺寸的减小导致NoC的故障发生率越来越高.针对传统NoC容错算法中容错路由路径过长的问题,提出了一种可重构容错路由算法.该算法基于扩展的细粒度功能故障模型,对邻节点的故障情况及时掌握,并结合新的路由端口优先级策略和奇偶转向模型,实现了数据包的无死锁最优化容错路由.实验表明,该算法的路由路径更接近于最短路由路径,同时以增加较少的硬件开销为代价,获得了更优的容错性能,并具有更低的延迟和更高的吞吐量.     

二维mesh上的自适应容错路由算法

基于故障块模型提出了二维ｍｅｓｈ上的自适应无死锁容错路由算法。该算法将网络分为两个虚拟网络ＶＩＮ０和ＶＩＮ１。消息根据源与目的节点的相对位置判断进入哪一个虚拟网络。消息在没有遇上故障时经由最短路径路由。算法的容错技术是基于故障环和故障链的概念。最后,将该算法与另一个二维ｍｅｓｈ上的容错路由算法ｆ－ｃｕｂｃ２进行性能比较。     

基于有故障区域的Mesh网络目标结点间的最短路由算法

Mesh网络是较早研究的且现在仍然是最为重要的、最有吸引力的网络模型之一。因其结构、规则简单及良好的可扩展性,易于VLSI(超大规模集成电路)的实现,网格(Mesh)网络不仅成为了许多理论研究的基础模型,而且也是许多大型多处理器并行计算机系统所采用的拓扑结构。给出了两种故障情形下的最短路由算法:1)当Mesh的行数大于等于3且列数大于等于3、出现一个矩形故障区域时,给出了任意两个无故障结点间的最短路由算法,并且计算出了路径长度；2)当Mesh的行数≥3且列数≥3、某个结点及其k跳以内的邻居结点出现故障时,给出了任意两个无故障结点间的最短路由算法,并且计算出了路径长度。     

蜂窝网络单点容错路由协议研究

容错路由是目前分布式系统热门的研究课题之一，然而目前大多数容错路由的相关研究，如Mesh、Hypercubes等，大都以mesh架构为主要环境。本论文提出了一个可在蜂窝网络架构上容忍一个错误节点的容错路由算法。若最短路径发生一个节点错误时。仍可以利用该算法找到一条近似最佳路径，它是利用在蜂窝网络的：起始点S与终点D两点坐标找出最短路径R，并将此路径以正规表示式表示，然后当发现路径中有节点故障时，则利用算法的caba=ba替换规则，绕过此错误节点。这就是本文在Honeycomb架构下提出的容错路由算法。     

All-To-All Personalized Communication in Wormhole-Routed 2D/3D Meshes and Multidimensional Interconnection Networks

2004.29计算机工程与应用1INTRODUCTIONInamessage-passingmulti-computernetwork,processorsoftenneedtocommunicatewitheachotherforvariousrea-sons,suchasloadbalancing,eventsynchronization,anddataexchange.Basedonthenumberofsendingandreceivingpro-cessors,thesecommunicationscanbeclassifiedintocommuni-cationpatternssuchasone-to-one(unicast),one-to-many(multicast),one-to-all(broadcast),andall-to-all.Thenatureofthemessagetobesentcanbeclassifiedaspersonalizedornon-personalized.Theall-to-allpersonalized…     

Randomized Partially-Minimal Routing on Three-Dimensional Mesh Networks

This letter presents a new oblivious routing algorithm for 3D mesh networks called Randomized Partially- Minimal (RPM) routing that provably achieves optimal worstcase throughput for 3D meshes when the network radix k is even and within a factor of 1/k2 of optimal when k is odd. Although this optimality result has been achieved with the minimal routing algorithm O1TURN [9] for the 2D case, the worst-case throughput of O1TURN degrades tremendously in higher dimensions. Other existing routing algorithms suffer from either poor worst-case throughput (DOR [10], ROMM [8]) or poor latency (VAL [14]). RPM on the other hand achieves near optimal worst-case and good average-case throughput as well as good latency performance.     

A survey of routing algorithm for mesh Network-on-Chip

With the rapid development of semiconductor industry, the number of cores integrated on chip increases quickly, which brings tough challenges such as bandwidth, scalability and power into on-chip interconnection. Under such background, Network-on-Chip (NoC) is proposed and gradually replacing the traditional on-chip interconnections such as sharing bus and crossbar. For the convenience of physical layout, mesh is the most used topology in NoC design. Routing algorithm, which decides the paths of packets, has significant impact on the latency and throughput of network. Thus routing algorithm plays a vital role in a wellperformed network. This study mainly focuses on the routing algorithms of mesh NoC. By whether taking network information into consideration in routing decision, routing algorithms of NoC can be roughly classified into oblivious routing and adaptive routing. Oblivious routing costs less without adaptiveness while adaptive routing is on the contrary. To combine the advantages of oblivious and adaptive routing algorithm, half-adaptive algorithms were proposed. In this paper, the concepts, taxonomy and features of routing algorithms of NoC are introduced. Then the importance of routing algorithms in mesh NoC is highlighted, and representative routing algorithms with respective features are reviewed and summarized. Finally, we try to shed light upon the future work of NoC routing algorithms.     

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     

Deadlock-free multicast wormhole routing in 2-D mesh multicomputers

Multicast communication services, in which the same message is delivered from a source node to an arbitrary number of destination nodes, are being provided in new-generation multicomputers. Broadcast is a special case of multicast in which a message is delivered to all nodes in the network. The nCUBE-2, a wormhole-routed hypercube multicomputer, provides hardware support for broadcast and a restricted form of multicast in which the destinations form a subcube. However, the broadcast routing algorithm adopted in the nCUBE-2 is not deadlock-free. In this paper, four multicast wormhole routing strategies for 2-D mesh multicomputers are proposed and studied. All of the algorithms are shown to be deadlock-free. These are the first deadlock-free multicast wormhole routing algorithms ever proposed. A simulation study has been conducted that compares the performance of these multicast algorithms under dynamic network traffic conditions in a 2-D mesh. The results indicate that a dual-path routing algorithm offers performance advantages over tree-based, multipath, and fixed-path algorithms     

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     

3D hexagonal network: modeling, topological properties, addressing scheme, and optimal routing algorithm

The 2D hexagonal mesh, based on triangle plane tessellation, is considered as a multiprocessor interconnection network. The 3D hexagonal mesh is presented as a natural extension of the hexagonal mesh. Although the topological properties of the 2D hexagonal mesh are well known, existing addressing schemes are not suitable to be extended to 3D hexagonal mesh. Then, we present, in this paper, a new addressing scheme and an optimal routing algorithm for 2D hexagonal network based on the distance formula and using shortest paths. We propose also a 3D hexagonal network that can be built with 2D hexagonal meshes as a natural generalization. We also present some topological properties, an efficient addressing scheme, and an optimal routing algorithm based on our 2D routing algorithm.     

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     

Incremental design of scalable interconnection networks using basic building blocks

In this paper, we present an incremental design of scalable interconnection networks in multicomputer systems using basic building blocks. Both network topologies and routing algorithms are considered. We use wormhole-routed small-scale 2D meshes as basic building blocks. The minimum requirement to expand these networks is a single building block. This implies that the network does not have to maintain the regular 2D mesh topology. Some new topologies are introduced: incomplete meshes based on those adaptive routing algorithms designed from the turn model and extended incomplete meshes based on XY routing. We show that the original routing algorithm can be adopted to send a message between any source and destination without using store-and-forward and causing deadlock. The way that the network is constructed incrementally requires no or a very small amount of rewiring and keeps high bisection density and short diameter of the network. The design methods can be used to economically and incrementally build expandable and scalable parallel computers.     

多优先级自适应片上网络路由算法设计

提出一种适用于二维网格结构的片上网络(NoC)路由算法,该算法具有自适应性与最短路径的特点.采用多种优先级对数据进行裁决并传输,能提高系统的吞吐量,降低网络延迟.通过采用NIRGAM仿真平台对算法进行仿真,在4×4网格结构下,与其他NoC路由算法进行性能对比,结果显示该算法在热点模式下具有优势.