Fault-tolerant wormhole routing for hypercube networks

We present an adaptive fault-tolerant wormhole routing algorithm for hypercubes by using 3 virtual networks. The routing algorithm can tolerate at least n−1 faulty nodes and can route a message via a path of length no more than the shortest path plus four. Previous algorithms which achieve the same fault tolerant ability need 5 virtual networks. Simulation results are also given in this paper.     

Adaptive routing protocols for hypercube interconnection networks

A taxonomy for characterizing adaptive routing protocols for hypercube interconnection networks (HINs) is presented. The taxonomy is based on classes of routing decisions common to any HIN. This taxonomy is used to discuss existing and proposed protocols. Rather than an exhaustive enumeration of related research, the protocols selected for discussion are intended to be representative of the classes defined by the taxonomy. These protocols are candidates for use in massively parallel architectures configured with HINs. To provide some insight into their behavior in very large HINs, results of simulation studies of representative protocols are presented     

Parallel routing algorithms for incomplete hypercube interconnection networks

Hypercube interconnection networks have been receiving considerable attention in the supercomputing environment. However, the number of processors must be exactly 2^r for an r-cube complete hypercube. This restriction severely limits its applicability. In this paper, we address three variant hypercube topologies with more flexibility in system sizes, the labelled hypercubes I_m^r, I_M^r, and I_A^r. Incomplete hypercube I_m^r consists of an r-cube and an m-cube complete hypercubes; I_m^r is composed of 2^r and Σ_{m ε M} 2^m nodes; I_Ar comes from an r-cube complete hypercube which operates in a degraded manner and allows that the missing nodes to be arbitrarily distributed. Specifically, we focus on the parallel paths routing algorithms for these three classes of incomplete hypercubes. Parallel paths between any given two nodes mean that these paths have the same source and destination nodes but with different intermediate nodes. Parallel communication is important as it will allow us to use the full bandwidth of the multiprocessors for the data transfer operation between any two nodes, and3these redundant paths can increase system fault-tolerance and communication reliability. With these parallel routing algorithms, one can use them as a criterion to design multiprocessor systems.     

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     

Fault-tolerant routing in hypercube multicomputers using local safety information

This paper studies fault-tolerant routing for injured hypercubes using local safety information. It is shown that a minimum feasible path is always available if the spanning subcube that contains both source and destination is safe. The safety information outside the spanning subcube is applied only when derouting is needed. A routing scheme based on local safety information is proposed and the extra cost to obtain local safety information is comparable to the one based on global safety information. The proposed algorithm guarantees to find a minimum feasible path if the spanning subcube is contained in a maximal safe subcube and the source is locally safe in the maximal safe subcube. A new technique to set up a partial path is proposed based on local safety information when the above conditions are not met. Sufficient simulation results are provided to demonstrate the effectiveness of the method by comparing with the previous methods.     

Finding cycles in hierarchical hypercube networks

The hierarchical hypercube network, which was proposed as an alternative to the hypercube, is suitable for building a large-scale multiprocessor system. A bipartite graph G=(V,E) is bipancyclic if it contains cycles of all even lengths ranging from 4 to |V|. In this paper, we show that the hierarchical hypercube network is bipancyclic.     

An analysis of cube-connected cycles and circular shuffle networks for parallel computation

This paper is concerned with demonstrating isomorphism between two classes of computer architectures that support parallel computation, viz., the cube-connected cycles (CCC) network and the homogeneous circular shuffle network (HCSN). This is done by developing a suitable and common notation for addressing processing elements and specifying interconnections in the two networks. The implications of such an equivalence are discussed. Properties and algorithms concerning HCSN networks, with respect to routing and fault tolerance, thereby, immediately become applicable to CCC networks. As for HCSN networks, their VLSI layout is now apparent. The networks are shown to be totally symmetric with respect to each processor, and in some cases may be recursively defined in terms of modules. Further, any algorithm that runs on an HCSN network also runs on a CCC network without any modification. It is also shown that a large class of algorithms that run on a CCC network can be implemented, with slight modification, on an HCSN network. In particular, an implementation of the DESCENT algorithm on an HCSN network is proposed.     

故障超立方体网络中的路由算法

针对超立方体结构的多处理机系统中存在故障的情况,提出了一个应用于超立方体网络的容错路由算法。该容错路由算法是基于局部信息的,只需要知道邻节点的状态,而无需知道整个网络的运行情况。对于给定的源节点和目的节点,路由算法均能够找到一条最优通路,并且可以预防死锁。模拟实验结果表明,路由算法所构造的路径长度接近于两个节点之间的最优路径长度。     

An optimal multicast algorithm for cube-connected cycles

This paper presents an efficient algorithm that implements one-to-many,or multicast,communication in one-port wormhole-routed cube-connected cycles(CCCs) in the absence of hardware multicast support.By exploiting the propoeries of the switching technology and the use of virtual channels,a minimumtime multicast algorithm is presented for n-dimensional CCCs that use deterministic routing of unicast messages.The algorithm can deliver a multicast message to m-1 destinations in [log2m] message-passing steps,while avoiding contention among the constitutent unicast messages,Performance results of a simulation study on CCCs with up to 10,240 nodes are also given.     

Load balancing and routing on the hypercube and related networks

Several results related to the load balancing problem on the hypercube, the shuffle-exchange, the cube-connected cycles, and the butterfly are shown. Implications of these results for routing algorithms are also discussed. Our results include the following:

• Efficient load balancing algorithms are found for the hypercube, the shuffle-exchange, the cube-connected cycles, and the butterfly.

• Load balancing is shown to require more time on a p-processor shuffle-exchange, cube-connected cycle or butterfly than on a p-processor weak hypercube.

• Routing n packets on a p-processor hypercube can be done optimally whenever n = p^1+1/k, for any fixed k > 0.

     

A testbed for evaluation of fault-tolerant routing inmultiprocessor interconnection networks

This paper presents a comprehensive evaluation testbed for interconnection networks and routing algorithms using real applications. The testbed is flexible enough to implement any network topology and fault-tolerant routing algorithm, and allows the system architect to study the cost versus performance trade-offs for a range of network parameters. We illustrate its use with one fault-tolerant algorithm and analyze the performance of four shared memory applications with different fault conditions. We also show how the testbed can be used to drive future research in fault-tolerant routing algorithms and architectures by proposing and evaluating novel architectural enhancements to the network router, called path selection heuristics (PSH). We propose three such schemes and the Least Recently Used (LRU) PSH is shown to give the best performance in the presence of faults     

Performance analysis of mesh interconnection networks withdeterministic routing

This paper develops detailed analytical performance models for k-ary n-cube networks with single-hit or infinite buffers, wormhole routing, and the nonadaptive deadlock-free routing scheme proposed by Dally and Seitz (1987). In contrast to previous performance studies of such networks, the system is modeled as a closed queueing network that: includes the effects of blocking and pipelining of messages in the network; allows for arbitrary source-destination probability distributions; and explicitly models the virtual channels used in the deadlock-free routing algorithm. The models are used to examine several performance issues for 2-D networks with shared-memory traffic. These results should prove useful for engineering high-performance systems based on low-dimensional k-ary n-cube networks     

On multistage interconnection networks with small clock cycles

In packet switching using multistage interconnection networks (MIN's), it is generally assumed that the packet movements successively propagate from the last stage to the first stage in one network cycle. Ding and Bhuyan (1994), however, have shown that the network performance can be significantly improved if the packet movements are confined within each pair of adjacent stages using small clock cycles. In this short note, we present a model for estimating the performance of multibuffered MIN's employing the approach. Using the model, the relative effectiveness of the approach is identified compared to the traditional design     

交换超立方体网络容错路由研究

为了研究交换超立方体网络容错路由问题,引入了相邻结点集合类的概念,提出了相邻结点集的求解公式。对于满足任意子连通性条件的交换超立方体网络,给出了基于相邻结点集合类的自适应容错路由算法及算法的步长上界。仿真实验结果表明算法是有效的。     

超立方体网络下的自适应容错路由研究*

针对超立方体结构的多处理机系统出现故障的问题,对容错超立方体网络的局部连通性进行了研究。根据局部连通性的特点定义了相邻节点集合类的概念,提出并证明了求解两类相邻节点集合的公式。给出了满足任意子连通性条件的超立方体网络的自适应容错路由算法。该算法是分布式和基于局部信息的,可以预防死锁。仿真实验的结果表明算法是高效的,且构建的路径长度接近于最优路径长度。     

直连网络中的动态自适应容错路由算法

针对超级计算机的直连网络发生链路或节点故障,需要在保证一定网络性能的前提下在线完成网络重构的问题,提出一种直连网络中的动态自适应容错路由算法.该算法能够承受空间和时间上任何数目故障的组合,使发生故障的系统经过自动重构后能够维持较优的计算能力.该算法不牺牲任何健康节点,并且无需过多硬件资源.模拟结果表明,在网络无故障的情况下几乎不影响直连网络的性能,数据结果也表明了故障恢复的实时性和有效性.     

A new hierarchy of hypercube interconnection schemes for parallel computers

This paper introduces a new hierarchy of cube-based interconnection schemes, called the base-b cube (which properly contains the well-known binary cube), for the design of parallel computers. This hierarchy admits a recursive definition and allows many more reconfigurations than are possible with the binary cube. Our analysis addresses the inherent cost-delay trade-off for this hierarchy along with a number of related topological properties such as sparsity, diameter, existence of node disjoint paths, and odd and even cycles. Embeddings of standard interconnection schemes including linear and two-dimensional arrays, rings, and complete binary trees in a base-b cube are illustrated.     

Fast algorithms for bit-serial routing on a hypercube

In this paper we describe anO(logN)-bit-step randomized algorithm for bit-serial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of on-line circuit switching in anO(1)-dilated hypercube (i.e., the problem of establishing edge-disjoint paths between the nodes of the dilated hypercube for any one-to-one mapping).Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the Borodin-Hopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least (log² N/log logN) bit steps with high probability for almost all permutations.This research was supported by the Defense Advanced Research Projects Agency under Contracts N00014-87-K-825 and N00014-89-J-1988, the Air Force under Contract AFOSR-89-0271, and the Army under Contract DAAL-03-86-K-0171. This work was completed while the third and fourth authors were at the Laboratory for Computer Science, Massachusetts Institute of Technology.