Work Efficient Hashing on Parallel and Vector Computers

Parallel hashing is well-known in the folklore of parallel computing, but there has been a remarkable dearth of literature describing it in detail. Because many parallel algorithms such as histogramming, set intersection and dictionary lookup can make use of hashing as a core step, hashing is a fundamental parallel operation. This paper sheds light on the performance that may be achieved using parallel hashing algorithms and should lend credibility to their use.

Computational fluid dynamics on parallel processors

A massively parallel knowledge-base server using a hypercube multiprocessor

Two new parallel integer sorting algorithms, queue-sort and barrel-sort, are presented and analyzed in detail. These algorithms do not have optimal parallel complexity, yet they show very good performance in practice. Queue-sort designed for fine-scale parallel architectures which allow the queueing of multiple messages to the same destination. Barrel-sort is designed for medium-scale parallel architectures with a high message passing overhead. The performance results from the implementation of queue-sort on a Connection Machine CM-2 and barrel-sort on a 128 processor iPSC/860 are given. The two implementations are found to be comparable in performance but not as good as a fully vectorized bucket sort on the Cray YMP.

The authors have developed a formulation of the phase problem of X-ray crystallography in terms of a minimal function of phases and a new minimization algorithm called shake-and-bake for solving this minimal function. The implementation details of the shake-and-bake strategy on the Connection Machine CM-2 are presented. The shake-and-bake algorithm has been used to determine the atomic structure of four test structures, ranging from 28 to 317 atoms. These results indicate that shake-and-bake is effective on structures of this size. >

This paper presents three traffic network simulation models implemented on massively parallel computer, the Connection Machine CM-2. The proposed simulation models have been parallelized to take advantage of the parallel computers since they can offer the required computational power at an economical cost/performance ratio. The paper presents detailed discussion of parallel data structure and parallel logic for each simulation model. Several simulation experiments have been carried out to compare the execution speed of each methodology. The preliminary research results indicate that parallel computing architecture offers a very promising alternative for the implementation of real-time traffic simulation.

A novel massively parallel technique for rigorous simulation of topography scattering in optical lithography has been developed and tested. The method is equivalent to the time-domain finite-difference method (TDFDM) used in electromagnetic scattering simulations, but exploits the parallel nature of wave propagation and the power of recent massively parallel architectures such as the Connection Machine. A working code called TEMPEST has been implemented on a Connection Machine CM-2 having 1 to 32 K processors with up to 1 M virtual processors. Numerical accuracy comparable with that of other fully rigorous methods was achieved. A very significant finding was that the solution required constant time per iteration for problems ranging from a few thousand unknowns up to one million, provided the ratio between the problem size and the number of processors is kept constant. The suitability of TEMPEST for solving a large class of topography structures important in alignment, metrology, and lithography is illustrated by examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The application of parallel computers to reservoir simulation is studied with the aid of two recently introduced Multiple Instruction, Multiple Data (MIMD) computers. The problems posed by reservoir simulators are shown to be particularly well suited for such parallel computers* Fundamental parallel programming techniques using Fortran are presented for the Hetrogeneous Element Processor (HEP) produced by Denelcor and the iPSC Hypercube produced by Intel. These techniques are then applied to two of the most time consuming tasks in reservoir simulation: forming the matrix coefficients and producing a sparse matrix solution. The problem of parallel formation of sparse matrix coefficients is addressed for the single and multiphase cases using both black oil and compositional fluid models. Parallel sparse matrix solution is addressed by considering D4 ordered Gaussian elimination, and the multigrid, conjugate gradient, and Successive Over-Relaxation (SOR) methods. Three parallel algorithms based on SOR are developed to illustrate the possible diversity of parallel algorithms. The red-black and multicolored SOR methods which are often used on vector machines are shown to be easily adaptable to parallel MIMD machine. Matrix partitioning and a new method of iteration pipelining are also presented as parallel SOR methods. The various SOR algorithms, in parallel form, are mapped onto the HEP to illustrate the speedups currently possible on an MIMD machine. Projections are made on the future importance of these types of machines to reservoir simulation.

The Society of Exploration Geophysicists (SEG) ha! defined a subroutine standard for seismic signa processing. Most of the subroutines described in the SEC standard perform very elementary operations (such a! adding two vectors) which are similar to array processor! calls. Ease of programming, standardization, am portability, resulting in higher efficiency of compiled code are the goals of these subroutines. The Connection Machine CM-2 is a data paralle computing system comprised of up to 65,536 (64K: processors. Each of the processors has 8 kilobytes o: memory associated with it as well as several flags. Tht Connection Machine is designed to deal with large-scab problems such as processing the huge amounts of datz that occur in seismic data processing. This paper describer an exploratory implementation of the Seismic Subroutim Standard (SSS) and studies the performance and adequacy of codes on the Connection Machine that contain calls tc the SEG.

In this paper, we propose a method for solving visibility-based terrain path planning problems for groups of vehicles using data parallel machines. The discussion focuses on path planning for two groups of vehicles so that they move in a bounding overwatch manner. Furthermore, the planned paths for the vehicles themselves are subject to intervisibility constraints, configuration constraints, and different terrain traversabilities due to variations in terrain type and slope. A spatial-temporal sampling approach is adopted to discretize the solution space and facilitate fast computation on a data parallel machine. One of the key computations in the planning is the region-to-region visibility analysis, which is computationally expensive but essential to the choice of subgoals to carry out reconnaissance activities. A parallel algorithm for this analysis is developed. By reducing the communication complexity, our algorithm achieves much faster running time than traditional methods. The algorithms are implemented on a Connection Machine CM-2, and the experimental results show that the planning system effectively generates good paths.

The direct method for solving N-body problems maps perfectly onto hypercube architectures. Unlike other hypercube implementations, we have implemented a direct N-body solver on the Connection Machine CM-2 which makes optimum use of the full bandwidth of the hypercube. When N > P, where P is the number of floating-point processors, the communication time of the algorithm is negligible, and the execution time is that of the arithmetic time giving a P-fold speed-up for real problems. To obtain this performance, we use “rotated and translated Gray codes” which result in time-wise edge disjoint Hamiltonian paths on the hypercube. We further propose that this communication pattern has unexplored potential for other types of algorithms. Timings are presented for a collection of interacting point vortices in two dimensions. The computation of the velocities of 14,000 vortices in 32-bit precision takes 2 seconds on a 16K CM-2.

This paper discusses the massively parallel solution of linear network programs. It integrates the general algorithmic framework of proximal minimization with D-functions (PMD) with primal-dual row-action algorithms. Three alternative algorithmic schemes are studied: quadratic proximal point, entropic proximal point, and least 2-norm perturbations. Each is solving a linear network problem by solving a sequence of nonlinear approximations. The nonlinear subproblems decompose for massively parallel computing. The three algorithms are implemented on a Connection Machine CM-2 with up to 32K processing elements, and problems with up to 16 million variables are solved. A comparison of the three algorithms establishes their relative efficiency. Numerical experiments also establish the best internal tactics which can be used when implementing proximal minimization algorithms. Finally, the new algorithms are compared with an implementation of the network simplex algorithm executing on a CRAY Y-MP vector supercomputer.

On the Leaving Coefficients of Real Many-Variable Polynomials

An implementation of the Car–Parrinello algorithm for total energy pseudopotential calculations is undertaken on a massively parallel supercomputer, the Connection Machine CM-2. Its large memory and throughput makes feasible computations with systems involving more atoms than previously possible on conventional vector supercomputers. Calculations of the Takayanagi 7×7 reconstruction of the Si(111) surface demonstrate that computations involving 1000 atoms at realistic cutoff energies are now possible using ab initio techniques.

In this paper we describe a linear time algorithm using O(n2) processors for computing the fragment vector in Steiner triple systems. The algorithm is designed for SIMD machine having a grid interconnection network. We show the implementation and some experimental results obtained on the Connection Machine CM-2.