A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

The Honeycomb Architecture: Prototype Analysis and Design

Due to the inherent potential of parallel processing, a lot of attention has focused on massively parallel computer architecture. To a large extent, the performance of a massively parallel architecture is a function of the flexibility of its communication network. The ability to configure the topology of the machine determines the ease with which problems are mapped onto the architecture. If the machine is sufficiently flexible, the architecture can be configured to match the natural structure of a wide range of problems. There are essentially four unique types of massively parallel architectures: 1. Cellular Arrays 2. Lattice Architectures [21, 30] 3. Connection Architectures [19] 4. Honeycomb Architectures [24] All four architectures are classified as SIMD. Each, however, offers a slightly different solution to the mapping problem. The first three approaches are characterized by easily distinguishable processor, communication, and memory components. In contrast, the Honeycomb architecture contains multipurpose processing/communication/memory cells. Each cell can function as either a simple CPU, a memory cell, or an element of a communication bus. The conventional approach to massive parallelism is the cellular array. It typically consists of an array of processing elements arranged in a mesh pattern with hard wired connections between neighboring processors. Due to their fixed topology, cellular arrays impose severe limitations upon interprocessor communication. The lattice architecture is a somewhat more flexible approach to massive parallelism. It consists of a lattice of processing elements embedded in an array of simple switching elements. The switching elements form a programmable interconnection network. A lattice architecture can be configured in a number of different topologies, but it is still only a partial solution to the mapping problem. The connection architecture offers a comprehensive solution to the mapping problem. It consists of a cellular array integrated into a packet-switched communication network. The network provides transparent communication between all processing elements. Note that the communication network is physically abstracted from the processor array, allowing the processors to evolve independently of the network. The Honeycomb architecture offers a unique solution to the mapping problem. It consists of an array of identical processing/communication/memory cells. Each cell can function as either a processor cell, a communication cell, or a memory cell. Collections of Honeycomb cells can be grouped into multicell CPUs, multi-cell memories, or multi-cell CPU-memory systems. Multi-cell CPU-memory systems are hereafter referred to as processing clusters. The topology of the Honeycomb is determined at compilation time. During a preprocessing phase, the Honeycomb is adjusted to the desired topology. The Honeycomb cell is extremely simple, capable of only simple arithmetic and logic operations. The simplicity of the Honeycomb cell is the key to the Honeycomb concept. As indicated in [24], there are two main research avenues to pursue in furthering the Honeycomb concept: 1. Analyzing the design of a uniform Honeycomb cell 2. Mapping algorithms onto the Honeycomb architecture This technical report concentrates on the first issue. While alluded to throughout the report, the second issue is not addressed in any detail

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified

Efficient parallel processing with optical interconnections

With the advances in VLSI technology, it is now possible to build chips which can each contain thousands of processors. The efficiency of such chips in executing parallel algorithms heavily depends on the interconnection topology of the processors. It is not possible to build a fully interconnected network of processors with constant fan-in/fan-out using electrical interconnections. Free space optics is a remedy to this limitation. Qualities exclusive to the optical medium are its ability to be directed for propagation in free space and the property that optical channels can cross in space without any interference. In this thesis, we present an electro-optical interconnected architecture named Optical Reconfigurable Mesh (ORM). It is based on an existing optical model of computation. There are two layers in the architecture. The processing layer is a reconfigurable mesh and the deflecting layer contains optical devices to deflect light beams. ORM provides three types of communication mechanisms. The first is for arbitrary planar connections among sets of locally connected processors using the reconfigurable mesh. The second is for arbitrary connections among N of the processors using the electrical buses on the processing layer and N2 fixed passive deflecting units on the deflection layer. The third is for arbitrary connections among any of the N2 processors using the N2 mechanically reconfigurable deflectors in the deflection layer. The third type of communication mechanisms is significantly slower than the other two. Therefore, it is desirable to avoid reconfiguring this type of communication during the execution of the algorithms. Instead, the optical reconfiguration can be done before the execution of each algorithm begins. Determining a right configuration that would be suitable for the entire configuration of a task execution is studied in this thesis. The basic data movements for each of the mechanisms are studied. Finally, to show the power of ORM, we use all three types of communication mechanisms in the first O(logN) time algorithm for finding the convex hulls of all figures in an N x N binary image presented in this thesis

Efficient Mapping of Neural Network Models on a Class of Parallel Architectures.

This dissertation develops a formal and systematic methodology for efficient mapping of several contemporary artificial neural network (ANN) models on k-ary n-cube parallel architectures (KNC\u27s). We apply the general mapping to several important ANN models including feedforward ANN\u27s trained with backpropagation algorithm, radial basis function networks, cascade correlation learning, and adaptive resonance theory networks. Our approach utilizes a parallel task graph representing concurrent operations of the ANN model during training. The mapping of the ANN is performed in two steps. First, the parallel task graph of the ANN is mapped to a virtual KNC of compatible dimensionality. This involves decomposing each operation into its atomic tasks. Second, the dimensionality of the virtual KNC architecture is recursively reduced through a sequence of transformations until a desired metric is optimized. We refer to this process as folding the virtual architecture. The optimization criteria we consider in this dissertation are defined in terms of the iteration time of the algorithm on the folded architecture. If necessary, the mapping scheme may utilize a subset of the processors of a given KNC architecture if it results in the most efficient simulation. A unique feature of our mapping is that it systematically selects an appropriate degree of parallelism leading to a highly efficient realization of the ANN model on KNC architectures. A novel feature of our work is its ability to efficiently map unit-allocating ANN\u27s. These networks possess a dynamic structure which grows during training. We present a highly efficient scheme for simulating such networks on existing KNC parallel architectures. We assume an upper bound on size of the neural network We perform the folding such that the iteration time of the largest network is minimized. We show that our mapping leads to near-optimal simulation of smaller instances of the neural network. In addition, based on our mapping no data migration or task rescheduling is needed as the size of network grows

Data broadcasting and reduction, prefix computation, and sorting on reduced hypercube (RH) parallel computers

The binary hypercube parallel computer has been very popular due to its rich interconnection structure and small average internode distance which allow the efficient embedding of frequently used topologies. Communication patterns of many parallel algorithms also match the hypercube topology. The hypercube has high VLSI complexity. however. due to the logarithmic increase in the number of connections to each node with the increase in the number of dimensions of the hypercube. The reduced hypercube (RH) interconnection network. which is obtained by a uniform reduction in the number of links for each hypercube node. yields lower-complexity interconnection networks when compared to hypercubes with the same number of nodes. It has been shown elsewhere that the RH interconnection network achieves performance comparable to that of the hypercube. at lower hardware cost. The reduced VLSI complexity of the RH also permits the construction of larger systems. thus. making the RH suitable for massively parallel processing. This thesis proposes algorithms for data broadcasting and reduction. prefix computation, and sorting on the RH parallel computer. All these operations are fundamental to many parallel algorithms. A worst case analysis of each algorithm is given and compared with equivalent- algorithms for the regular hypercube. It is shown that the proposed algorithms for the RH yield performance comparable to that for the regular hypercube