Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes

Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First we prove that the folded hypercube is optimal in the sense that only a single wildcard dimension can be added to the hypercube. We then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes we construct d-dimensional meshes and tori with wildcard dimensions. Finally, we show how these constructions can be used to tolerate edge and node faults in mesh and torus networks

Processor allocation strategies for modified hypercubes

Parallel processing has been widely accepted to be the future in high speed computing. Among the various parallel architectures proposed/implemented, the hypercube has shown a lot of promise because of its poweful properties, like regular topology, fault tolerance, low diameter, simple routing, and ability to efficiently emulate other architectures. The major drawback of the hypercube network is that it can not be expanded in practice because the number of communication ports for each processor grows as the logarithm of the total number of processors in the system. Therefore, once a hypercube supercomputer of a certain dimensionality has been built, any future expansions can be accomplished only by replacing the VLSI chips. This is an undesirable feature and a lot of work has been under progress to eliminate this stymie, thus providing a platform for easier expansion. Modified hypercubes (MHs) have been proposed as the building blocks of hypercube-based systems supporting incremental growth techniques without introducing extra resources for individual hypercubes. However, processor allocation on MHs proves to be a challenge due to a slight deviation in their topology from that of the standard hypercube network. This thesis addresses the issue of processor allocation on MHs and proposes various strategies which are based, partially or entirely, on table look-up approaches. A study of the various task allocation strategies for standard hypercubes is conducted and their suitability for MHs is evaluated. It is shown that the proposed strategies have a perfect subcube recognition ability and a superior performance. Existing processor allocation strategies for pure hypercube networks are demonstrated to be ineffective for MHs, in the light of their inability to recognize all available subcubes. A comparative analysis that involves the buddy strategy and the new strategies is carried out using simulation results

Partial multinode broadcast and partial exchange algorithms for d-dimensional meshes

Caption title. "Revision of January 1992."Includes bibliographical references (p. 24-26).Supported by NSF. NSF-ECS-8519058 Supported by ARO. DAAL03-86-K-0171by Emmanouel A. Varvarigos and Dimitri P. Bertsekas

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Off-chip Communications Architectures For High Throughput Network Processors

In this work, we present off-chip communications architectures for line cards to increase the throughput of the currently used memory system. In recent years there is a significant increase in memory bandwidth demand on line cards as a result of higher line rates, an increase in deep packet inspection operations and an unstoppable expansion in lookup tables. As line-rate data and NPU processing power increase, memory access time becomes the main system bottleneck during data store/retrieve operations. The growing demand for memory bandwidth contrasts the notion of indirect interconnect methodologies. Moreover, solutions to the memory bandwidth bottleneck are limited by physical constraints such as area and NPU I/O pins. Therefore, indirect interconnects are replaced with direct, packet-based networks such as mesh, torus or k-ary n-cubes. We investigate multiple k-ary n-cube based interconnects and propose two variations of 2-ary 3-cube interconnect called the 3D-bus and 3D-mesh. All of the k-ary n-cube interconnects include multiple, highly efficient techniques to route, switch, and control packet flows in order to minimize congestion spots and packet loss. We explore the tradeoffs between implementation constraints and performance. We also developed an event-driven, interconnect simulation framework to evaluate the performance of packet-based off-chip k-ary n-cube interconnect architectures for line cards. The simulator uses the state-of-the-art software design techniques to provide the user with a flexible yet robust tool, that can emulate multiple interconnect architectures under non-uniform traffic patterns. Moreover, the simulator offers the user with full control over network parameters, performance enhancing features and simulation time frames that make the platform as identical as possible to the real line card physical and functional properties. By using our network simulator, we reveal the best processor-memory configuration, out of multiple configurations, that achieves optimal performance. Moreover, we explore how network enhancement techniques such as virtual channels and sub-channeling improve network latency and throughput. Our performance results show that k-ary n-cube topologies, and especially our modified version of 2-ary 3-cube interconnect - the 3D-mesh, significantly outperform existing line card interconnects and are able to sustain higher traffic loads. The flow control mechanism proved to extensively reduce hot-spots, load-balance areas of high traffic rate and achieve low transmission failure rate. Moreover, it can scale to adopt more memories and/or processors and as a result to increase the line card\u27s processing power