Interconnection Networks Embeddings and Efficient Parallel Computations.

To obtain a greater performance, many processors are allowed to cooperate to solve a single problem. These processors communicate via an interconnection network or a bus. The most essential function of the underlying interconnection network is the efficient interchanging of messages between processes in different processors. Parallel machines based on the hypercube topology have gained a great respect in parallel computation because of its many attractive properties. Many versions of the hypercube have been introduced by many researchers mainly to enhance communications. The twisted hypercube is one of the most attractive versions of the hypercube. It preserves the important features of the hypercube and reduces its diameter by a factor of two. This dissertation investigates relations and transformations between various interconnection networks and the twisted hypercube and explore its efficiency in parallel computation. The capability of the twisted hypercube to simulate complete binary trees, complete quad trees, and rings is demonstrated and compared with the hypercube. Finally, the fault-tolerance of the twisted hypercube is investigated. We present optimal algorithms to simulate rings in a faulty twisted hypercube environment and compare that with the hypercube

CCL: a portable and tunable collective communication library for scalable parallel computers

A collective communication library for parallel computers includes frequently used operations such as broadcast, reduce, scatter, gather, concatenate, synchronize, and shift. Such a library provides users with a convenient programming interface, efficient communication operations, and the advantage of portability. A library of this nature, the Collective Communication Library (CCL), intended for the line of scalable parallel computer products by IBM, has been designed. CCL is part of the parallel application programming interface of the recently announced IBM 9076 Scalable POWERparallel System 1 (SP1). In this paper, we examine several issues related to the functionality, correctness, and performance of a portable collective communication library while focusing on three novel aspects in the design and implementation of CCL: 1) the introduction of process groups, 2) the definition of semantics that ensures correctness, and 3) the design of new and tunable algorithms based on a realistic point-to-point communication model

Fault-tolerant meshes with minimal numbers of spares

This paper presents several techniques for adding fault-tolerance to distributed memory parallel computers. More formally, given a target graph with n nodes, we create a fault-tolerant graph with n + k nodes such that given any set of k or fewer faulty nodes, the remaining graph is guaranteed to contain the target graph as a fault-free subgraph. As a result, any algorithm designed for the target graph will run with no slowdown in the presence of k or fewer node faults, regardless of their distribution. We present fault-tolerant graphs for target graphs which are 2-dimensional meshes, tori, eight-connected meshes and hexagonal meshes. In all cases our fault-tolerant graphs have smaller degree than any previously known graphs with the same properties

Embedding Meshes on the Star Graph

We develop algorithms for mapping n-dimensional meshes on a star graph of degree n with expansion 1 and dilation 3. We show that an n degree star graph can efficiently simulate an n-dimensional mesh

Efficient hypercube communications

Hypercube algorithms may be developed for a variety of communication-intensive tasks such as sending a message from one node to another, broadcasting a message from one node to all others, broadcasting a message from each node to all others, all-to-all personalized communication, one-to-all personalized communication, and exchanging messages between nodes via fixed permutations. All these communication patterns are special cases of many-to-many personalized communication. The problem of many-to-many personalized communication is investigated here. Two routing algorithms for many-to-many personalized communication are presented here. The algorithms proposed yield very high performance with respect to the number of time steps and packet transmissions. The first algorithm yields high performance through attempts to equibalance the number of messages at intermediate nodes. This technique tries to avoid creating a bottleneck at any node and thus reduces the total communication time. The second algorithm yields high performance through one-step time-lookahead equibalancing. It chooses from the candidate intermediate nodes the one which will probably have the minimum number of messages in the next cycle

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant

Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given

Some Theoretical Results of Hypercube for Parallel Architecture

This paper surveys some theoretical results of the hypercube for design of VLSI architecture. The parallel computer including the hypercube multiprocessor will become a leading technology that supports efficient computation for large uncertain systems

Parallel Computation on Hypercube-Like Machines.

The hypercube interconnection network has been recognized to be very suitable for a parallel computing architecture due to its attractive topological properties. Recently, several modified hypercubes have been propose to improve the performance of a hypercube. This dissertation deals with two modified hypercubes, the X-hypercube and the Z-cube. The X-hypercube is a variant of the hypercube, with the same amount of hardware but a diameter of only $\lceil$(n + 1)/2$\rceil$ in a hypercube of dimension n. The Z-cube has only 75 percent of the edges of a hypercube with the same number vertices and the same diameter as the hypercube. In this dissertation, we investigate some topological properties and the effectiveness of the X-hypercube and the Z-cube in their combinatorial and computational aspects. We give the optimal or nearly optimal data communication algorithms including routing, broadcasting, and census function for the X-hypercube and the Z-cube. We also give the optimal embedding algorithms between the X-hypercube and the hypercube. It is shown that the average distance between vertices in a X-hypercube is roughly 13/16 of that in a hypercube. This implies that a X-hypercube achieves the better average communication performance than a hypercube. In addition, a set of fundamental SIMD algorithms for a X-hypercube is given. Our results indicate that the X-hypercube makes an improvement in performance over the hypercube, but not as much as the reduction in a diameter, and the Z-cube is a good alternative for the hypercube as far as the VLSI implementation is of major concern

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