A study of the communication cost of the FFT on torus multicomputers

The computation of a one-dimensional FFT on a c-dimensional torus multicomputer is analyzed. Different approaches are proposed which differ in the way they use the interconnection network. The first approach is based on the multidimensional index mapping technique for the FFT computation. The second approach starts from a hypercube algorithm and then embeds the hypercube onto the torus. The third approach reduces the communication cost of the hypercube algorithm by pipelining the communication operations. A novel methodology to pipeline the communication operations on a torus is proposed. Analytical models are presented to compare the different approaches. This comparison study shows that the best approach depends on the number of dimensions of the torus and the communication start-up and transfer times. The analytical models allow us to select the most efficient approach for the available machine.Peer ReviewedPostprint (published version

A network flow model for load balancing in circuit-switched multicomputers

In multicomputers that utilize circuit switching or wormhole routing, communication overhead depends largely on link contention - the variation due to distance between nodes is negligible. This has a major impact on the load balancing problem. In this case, there are some nodes with excess load (sources) and others with deficit load (sinks) and it is required to find a matching of sources to sinks that avoids contention. The problem is made complex by the hardwired routing on currently available machines: the user can control only which nodes communicate but not how the messages are routed. Network flow models of message flow in the mesh and the hypercube were developed to solve this problem. The crucial property of these models is the correspondence between minimum cost flows and correctly routed messages. To solve a given load balancing problem, a minimum cost flow algorithm is applied to the network. This permits one to determine efficiently a maximum contention free matching of sources to sinks which, in turn, tells one how much of the given imbalance can be eliminated without contention

Modeling and synthesis of multicomputer interconnection networks

The type of interconnection network employed has a profound effect on the performance of a multicomputer and multiprocessor design. Adequate models are needed to aid in the design and development of interconnection networks. A novel modeling approach using statistical and optimization techniques is described. This method represents an attempt to compare diverse interconnection network designs in a way that allows not only the best of existing designs to be identified but to suggest other, perhaps hybrid, networks that may offer better performance. Stepwise linear regression is used to develop a polynomial surface representation of performance in a (k+1) space with a total of k quantitative and qualitative independent variables describing graph-theoretic characteristics such as size, average degree, diameter, radius, girth, node-connectivity, edge-connectivity, minimum dominating set size, and maximum number of prime node and edge cutsets. Dependent variables used to measure performance are average message delay and the ratio of message completion rate to network connection cost. Response Surface Methodology (RSM) optimizes a response variable from a polynomial function of several independent variables. Steepest ascent path may also be used to approach optimum points

Hypercube algorithms on mesh connected multicomputers

A new methodology named CALMANT (CC-cube Algorithms on Meshes and Tori) for mapping a type of algorithm that we call CC-cube algorithm onto multicomputers with hypercube, mesh, or torus interconnection topology is proposed. This methodology is suitable when the initial problem can be expressed as a set of processes that communicate through a hypercube topology (a CC-cube algorithm). There are many important algorithms that fit into the CC-cube type. CALMANT is based on three different techniques: (a) the standard embedding to assign the processes of the algorithm to the nodes of the mesh multicomputer; (b) the communication pipelining technique to increase the level of communication parallelism inherent in the CC-cube algorithms; and (c) optimal message-scheduling algorithms proposed in this work in order to avoid conflicts and minimizing in this way the communication time. Although CALMANT is proposed for multicomputers with different interconnection network topologies, the paper only focuses on the particular case of meshes.Peer ReviewedPostprint (published version

Parallel Computers and Complex Systems

We present an overview of the state of the art and future trends in high performance parallel and distributed computing, and discuss techniques for using such computers in the simulation of complex problems in computational science. The use of high performance parallel computers can help improve our understanding of complex systems, and the converse is also true --- we can apply techniques used for the study of complex systems to improve our understanding of parallel computing. We consider parallel computing as the mapping of one complex system --- typically a model of the world --- into another complex system --- the parallel computer. We study static, dynamic, spatial and temporal properties of both the complex systems and the map between them. The result is a better understanding of which computer architectures are good for which problems, and of software structure, automatic partitioning of data, and the performance of parallel machines

Hyperswitch communication network

The Hyperswitch Communication Network (HCN) is a large scale parallel computer prototype being developed at JPL. Commercial versions of the HCN computer are planned. The HCN computer being designed is a message passing multiple instruction multiple data (MIMD) computer, and offers many advantages in price-performance ratio, reliability and availability, and manufacturing over traditional uniprocessors and bus based multiprocessors. The design of the HCN operating system is a uniquely flexible environment that combines both parallel processing and distributed processing. This programming paradigm can achieve a balance among the following competing factors: performance in processing and communications, user friendliness, and fault tolerance. The prototype is being designed to accommodate a maximum of 64 state of the art microprocessors. The HCN is classified as a distributed supercomputer. The HCN system is described, and the performance/cost analysis and other competing factors within the system design are reviewed

Parallel and distributed supercomputing at Caltech

Caltech uses parallel computers for a variety of large-scale scientific applications. It has acquired commercial parallel computers, some of which have performance that rivals or exceeds that of conventional, vector-oriented supercomputers. A new project has been started that builds on experience with concurrent computers and attempts to apply Caltech methods to the simultaneous use of parallel and vector supercomputers at four institutions that will be connected by a 800 Mb/s wide-area computer network. Distributed supercomputing experiments will be carried out on this testbed