Embedding cube-connected cycles graphs into faulty hypercubes

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults

Generalized hypercube structures and hyperswitch communication network

This paper discusses an ongoing study that uses a recent development in communication control technology to implement hybrid hypercube structures. These architectures are similar to binary hypercubes, but they also provide added connectivity between the processors. This added connectivity increases communication reliability while decreasing the latency of interprocessor message passing. Because these factors directly determine the speed that can be obtained by multiprocessor systems, these architectures are attractive for applications such as remote exploration and experimentation, where high performance and ultrareliability are required. This paper describes and enumerates these architectures and discusses how they can be implemented with a modified version of the hyperswitch communication network (HCN). The HCN is analyzed because it has three attractive features that enable these architectures to be effective: speed, fault tolerance, and the ability to pass multiple messages simultaneously through the same hyperswitch controller

A novel QoS multicast model in mobile ad hoc networks

2004-2005 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Hypercube-Based Topologies With Incremental Link Redundancy.

Hypercube structures have received a great deal of attention due to the attractive properties inherent to their topology. Parallel algorithms targeted at this topology can be partitioned into many tasks, each of which running on one node processor. A high degree of performance is achievable by running every task individually and concurrently on each node processor available in the hypercube. Nevertheless, the performance can be greatly degraded if the node processors spend much time just communicating with one another. The goal in designing hypercubes is, therefore, to achieve a high ratio of computation time to communication time. The dissertation addresses primarily ways to enhance system performance by minimizing the communication time among processors. The need for improving the performance of hypercube networks is clearly explained. Three novel topologies related to hypercubes with improved performance are proposed and analyzed. Firstly, the Bridged Hypercube (BHC) is introduced. It is shown that this design is remarkably more efficient and cost-effective than the standard hypercube due to its low diameter. Basic routing algorithms such as one to one and broadcasting are developed for the BHC and proven optimal. Shortcomings of the BHC such as its asymmetry and limited application are clearly discussed. The Folded Hypercube (FHC), a symmetric network with low diameter and low degree of the node, is introduced. This new topology is shown to support highly efficient communications among the processors. For the FHC, optimal routing algorithms are developed and proven to be remarkably more efficient than those of the conventional hypercube. For both BHC and FHC, network parameters such as average distance, message traffic density, and communication delay are derived and comparatively analyzed. Lastly, to enhance the fault tolerance of the hypercube, a new design called Fault Tolerant Hypercube (FTH) is proposed. The FTH is shown to exhibit a graceful degradation in performance with the existence of faults. Probabilistic models based on Markov chain are employed to characterize the fault tolerance of the FTH. The results are verified by Monte Carlo simulation. The most attractive feature of all new topologies is the asymptotically zero overhead associated with them. The designs are simple and implementable. These designs can lead themselves to many parallel processing applications requiring high degree of performance

Hamiltonian Decompositions of Regular Topology Networks with Convergence Routing

This paper introduces new methods to construct multiple virtual rings for loss-free routing of non-reserved bursty data in high-speed environments such as ATM LANs. The routing algorithm on multiple virtual rings is convergence routing which combines the actual routing decision with the internal flow control state. Multiple virtual rings are obtained on the hypercube and the circulant networks such that each virtual ring is hamiltonian, and are mutually edge-disjoint. It is shown that multiple virtual rings improve (i) the bound on the length of routing, and (ii) the fault tolerance. On the circulant graphs, necessary and sufficient conditions for hamiltonian decomposition is established. On the hypercube, three algorithms are designed for an N-node hypercube with even dimension: (i) an O(N) time algorithm to find two edge-disjoint hamiltonian circuits, (ii) an O(N log N) time algorithm to find I01N hamiltonian circuits with only E ~ 0.1 common edges, and (iii) a recursive algorithm for the hamiltonian decomposition of the hypercube with dimension power of two. It is shown analytically, and verified by simulations on the circulants that with the d virtual ring embeddings, a bound of O( N / d) is established on the maximum length of routing

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms