Connection Machine CM-2 Research Articles

PARALLEL INTEGER SORTING WITH MEDIUM AND FINE-SCALE PARALLELISM

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.

COMPUTATION OF THE SPATIAL STRING TENSION IN HIGH TEMPERATURE SU(2) GAUGE THEORY

A detailed investigation of the temperature dependence of the spatial string tension σs in SU(2) gauge theory is presented. A sustained performance of 3 GFLOPS on a 64K Connection Machine CM-2 equivalent has been achieved. Scaling of σs between β = 2.5115 and β = 2.74, on large lattices, is demonstrated. Below the critical temperature, Tc, σs remains constant. For temperatures larger than 2Tc the temperature dependence can be parametrized by σs(T) = (0.369 ± 0.014)2g4(T)T2, where g(T) is a 2-loop running coupling constant with the scale parameter determined as ΛT = (0.076 ± 0.013)Tc.

Massively parallel tabu search for the quadratic assignment problem

A new heuristic algorithm to perform tabu search on the Quadratic Assignment Problem (QAP) is developed. A massively parallel implementation of the algorithm on the Connection Machine CM-2 is provided. The implementation usesn2 processors, wheren is the size of the problem. The elements of the algorithm, calledPar_tabu, include dynamically changing tabu list sizes, aspiration criterion and long term memory. A new intensification strategy based on intermediate term memory is proposed and shown to be promising especially while solving large QAPs. The combination of all these elements gives a very efficient heuristic for the QAP: the best known or improved solutions are obtained in a significantly smaller number of iterations than in other comparative studies. Combined with the implementation on CM-2, this approach provides suboptimal solutions to QAPs of bigger dimensions in reasonable time.

DETERMINATION OF MONOPOLE CURRENT CLUSTERS IN FOUR-DIMENSIONAL QUANTUM ELECTRODYNAMICS

Magnetic monopole currents are believed to have a strong impact on the Monte Carlo dynamics of compact quantum electrodynamics near the phase transition. We have indications that updating algorithms have to form and to break up monopole current clusters in order to force the tunneling of the system between the coexisting phases, the confined phase and the Coulomb phase. This might be responsible for long lived metastabilities in the time series. We present parallel numerical algorithms which allow the fast identification of clusters of monopole loops, the determination of their topological properties as well as their visualization in the course of a Monte Carlo simulation. The algorithms are implemented on the Connection Machine CM-5. We compare the data parallel programming style with a message passing approach. Complexity and performance are discussed.

Parallel Computation of the Matrix of the Chemical Distances on the Connection Machine

Abstract We report here the parallel implementation of an original algorithm allowing a fast calculation of the distance matrix D of a graph representing a given chemical structure (molecule, polymer, crystal, etc.). Our algorithm fits perfectly in the SIMD parallel architecture of the Connection Machines CM-200 as we shall show. After discussing the performances of the parallel evaluation of D, we will end with a relevant application concerning C60 and C70 fullerenes. The present study applies to a generic globally connected graph without any restriction on the local connectivity of each graph's vertex.

Stochastic Dedication: Designing Fixed Income Portfolios Using Massively Parallel Benders Decomposition

Drawing on recent developments in discrete time fixed income options theory, we propose a stochastic programming procedure, which we call stochastic dedication, for managing asset/liability portfolios with interest rate contingent claims. The model uses scenario generation to combine deterministic dedication techniques with stochastic duration matching methods, and provides the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes. We employ a fixed income risk metric that can be interpreted as the fair market value of a collection of interest rate options that eliminates bankruptcy risk from the asset/liability portfolio. We incorporate this metric into a risk/return stochastic optimization model, using a binomial lattice sampling procedure to construct interest rate paths and cash flow streams from an arbitrage-free term structure model. The resulting parametric linear program has a particularly simple subproblem structure, and we have been able to solve it using resource-directed decomposition on a massively parallel computer system, the Connection Machine CM-2. We take a novel approach that uses a standard serial simplex method to solve the master problem, but generates scenarios and Benders cuts in a massively parallel manner. We discuss the performance of this implementation and present the results for a simple pension fund immunization problem.

Hypercube Algorithms for Direct N-Body Solvers for Different Granularities

Algorithms for the N-body problem are compared and contrasted, particularly those where N is in the range for which direct methods outperform approximation methods. With fewer bodies than processors, the so-called “replicated orrery” on a three-dimensional grid has been used successfully on the Connection Machine CM-2 architecture. With more bodies, the “rotated and translated Gray codes” is an ideal direct algorithm for machines such as the CM-2 in that it takes optimal advantage of the communications bandwidth of the machine.A classical Latin square can be used to abstractly denote any direct N-body calculation. Computational windows superimposed on this square illustrate the granularity of the computation. This point of view naturally illustrates a sequence of algorithms ranging along a granularity scale in the following order: “massively parallel,” “replicated orrery,” “orrery,” “rotated/translated Gray codes,” and “serial.”

Data parallel volume-rendering algorithms for interactive visualization

The increasing availability of parallel computing platforms has led to the development of parallel volume-rendering algorithms. In the present paper we compare two algorithms for volume raytracing in a data-parallel framework: a shearing technique and a line-drawing technique. The two algorithms are primarily distinguished by the level of parallelism they exploit. Both algorithms have been implemented on the Connection Machine CM2 massively parallel computer and execute at speeds suitable for interactive volume-rendering applications. Since considerable floating-point resources are available on the CM2, we have used rendering algorithms based on transport theory. In the second part of the paper we examine some of the tradeoffs involved between image quality and rendering speed when using high-fidelity rendering algorithms.

Multi-million particle molecular dynamics: III. Design considerations for data-parallel processing

This paper describes an implementation of a parallel molecular dynamics algorithm on the CM2 Connection Machine that is designed for large-scale simulations. The method employs a cell subdivision of the simulation region, and is partly based on the layer approach developed for vector processing. All communication is between adjacent processing elements, eliminating the need for global communication. Performance measurements were made with systems containing over 10 6 particles.

Implementation of a portable nested data-parallel language

This paper gives an overview of the implementation of NESL, a portable nested data-parallel language. This language and its implementation are the first to fully support nested data structures as well as nested data-parallel function calls. These features allow the concise description of parallel algorithms on irregular data, such as sparse matrices and graphs. In addition, they maintain the advantages of data-parallel languages: a simple programming model and portability. The current NESL implementation is based on an intermediate language called VCODE and a library of vector routines called CVL. It runs on the Connection Machine CM-2, the Cray Y-MP C90, and serial machines. We compare initial benchmark results of NESL with those of machine-specific code on these machines for three algorithms: least-squares line-fitting, median finding, and a sparse-matrix vector product. These results show that NESL's performance is competitive with that of machine-specific codes for regular dense data, and is often superior for irregular data.

Experience in using SIMD and MIMD parallelism for computational fluid dynamics

One of the key objectives of the Applied Research Branch in the Numerical Aerodynamic Simulation (NAS) Systems Division at NASA Ames Research Center is the accelerated introduction of highly parallel machines into a fully operational environment. In this report we summarize some of the experiences with the parallel testbed machines at the NAS Applied Research Branch. We discuss the performance results obtained from the implementation of two computational fluid dynamics (CFD) applications, an unstructured grid solver and a particle simulation, on the Connection Machine CM-2 and the Intel iPSC/860.

A model for portfolio management with mortgage-backed securities

We present a stochastic programming model for the management of large portfolios of mortgage-backed securities (abbreviated: MBS). It is a two-stage, multiperiod model, whereby portfolio decisions made here-and-now are influenced by uncertain information about the future. In particular, we consider uncertainty in both the prepayment activity of the MBSs in the portfolio, as well as uncertainty about the future reinvestment rates. A simulation procedure is used to generate interest rate paths and prepayment behavior, and the stochastic program can be extremely large. Solution of the resulting large-scale programs is particularly challenging. We show that with massively parallel computing technology, the proposed models are indeed solvable. Empirical results on a Connection Machine CM-2 are reported.

Implementation of the Car–Parrinello algorithm for ab initio total energy calculations on a massively parallel computer

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.

A Massively Parallel Algorithm for Nonlinear Stochastic Network Problems

We develop an algorithm for solving nonlinear, two-stage stochastic problems with network recourse. The algorithm is based on the framework of row-action methods. The problem is formulated by replicating the first-stage variables and then adding nonanticipativity side constraints. A series of (independent) deterministic network problems are solved at each step of the algorithm, followed by an iterative step over the nonanticipativity constraints. The solution point of the iterates over the nonanticipativity constraints is obtained analytically. The row-action nature of the algorithm makes it suitable for parallel implementations. A data representation of the problem is developed that permits the massively parallel solution of all the scenario subproblems concurrently. The algorithm is implemented on a Connection Machine CM-2 with up to 32K processing elements and achieves computing rates of 276 MFLOPS. Very large problems—8,192 scenarios with a deterministic equivalent nonlinear program with 868,367 constraints and 2,474,017 variables—are solved within a few minutes. We report extensive numerical results regarding the effects of stochasticity on the efficiency of the algorithm.

Proximal minimizations with D-functions and the massively parallel solution of linear network programs

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.

Simulating cardiac sinus and atrial network dynamics on the connection machine

Computational methods for simulating biophysically detailed, large-scale models of mammalian cardiac sinus and atrial networks on the massively parallel Connection Machine CM-2, and techniques for visualization of simulation data, are presented. Individual cells are modeled using the formulations of Noble et al. Models incorporate properties of voltage-dependent membrane currents, ion pumps and exchangers, and internal calcium sequestering and release mechanisms. Network models are used to investigate factors determining the site of generation and direction of propagation of the pacemaker potential. Models of the isolated sinus node are used to show that very few gap junction channels are required to support frequency entrainment. When cell membrane properties in the isolated sinus node models are modified to reproduce regional differences in oscillation properties, as described by the data of Kodama and Boyett, an excitatory wave is generated in the node periphery which propagates towards the node center. This agrees with activation patterns measured in the isolated sinus node by Kirchoff. When the model sinus node is surrounded by a region of atrial cells, the site of pacemaker potential generation is shifted away from the periphery towards the node center. This is in agreement with activation patterns measured by Kirchoff in the intact sinus node of the rabbit heart, and demonstrates the importance of sinus node boundary conditions on shaping the site of generation and direction of propagation of the pacemaker potential.

A Reformulation and Implementation of the Bryan-Cox-Semtner Ocean Model on the Connection Machine

Abstract Certain aspects of the Semtner-Chervin version of the Bryan-Cox-Semtner global ocean model are reformulated for improved efficiency on parallel computer architectures and on the Connection Machine CM-2 in particular. These changes involve (a) the switch from a streamfunction to a surface pressure formulation in the barotropic equations, (b) the splitting off of the Coriolis terms from the barotropic equations to produce a symmetric surface pressure equation, which then permits (c) the use of a preconditioned conjugate-gradient method for the solution of this equation. The switch to a surface pressure formulation (a) eliminates global equations associated with island boundary conditions and therefore improves performance as well as allows an unlimited number of islands, (b) reduces sensitivity to rapidly varying bottom topography and therefore obviates the need for smoothing the topography, and (c) makes the surface pressure a prognostic variable, thus potentially making it easier to assimilate su...

Using Distributed-Event Parallel Simulation to Study Departures from Many Queues in Series

In this paper we describe an application of distributed-event parallel simulation to study the transient behavior of a large non-Markovian network of queues. In particular, we implemented the parallel-prefix-based algorithm of Greenberg, Lubachevsky, and Mitrani [13,14] on the 8,192-processor CM-2 Connection machine and the 16,384-processor MasPar computer to simulate the departure times D(k, n) of the kth customer from the nth queue in a long series of single-server queues. Each queue has unlimited waiting space and uses the first-in first-out discipline. The service times of all the customers at all the queues are i.i.d. with a general distribution, and the system starts out with k customers in the first queue and all other queues empty. Glynn and Whitt [11] established limit theorems for this model, but very little could be said about the limits themselves. The simulation results presented here describe the limits and the quality of the approximations resulting from using the limits for finite k and n. Indeed, the simulations suggest interesting conjectures. For this model speeding up a single long run is far superior to independent replications, because very long runs are required to obtain unbiased estimates of the desired quantities and the variance of the estimator at the end of the run is small. The achieved simulation rate was about 17 billion service completions per hour, which is a speedup by about a factor of 100 compared to simulation on a conventional single-processor machine. This speedup contributed greatly to performing the desired experiments.

The running coupling from SU(3) gauge theory

We present high precision results on the static q q potential on 32 4 and smaller lattices, using the standard Wilson action at β = 6.0, 6.2, 6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (≈ 1%) we did not observe any finite size effects affecting the potential values, on varying the spatial lattice extent from 0.9 fm up to 3.3 fm. We find violations of asymptotic scaling in the bare coupling up to β = 6.8. We demonstrate that scaling violations on the string tension can be considerably reduced by introducing effective coupling schemes, which allow for a safer extrapolation of Λ L to its continuum value. We are also able to see and to quantify the running of the coupling from the interquark force. From this we extract the ratio √σ Λ L . Both methods yield consistent values for the Λ-parameter: Λ MS =0.558 +0.017 −0.007 × σ =246 +7 −3MeV .

Using Parallel Computers To Solve the Phase Problem of X-Ray Crystallography

Direct methods are commonly used by crystallogra phers to determine relatively small crystal structures. However, existing techniques do not appear to be ex tensible to larger structures. The recent development of a solution strategy called Shake-and-Bake, aimed at determining structures via local minimization and re peated Fourier transformations, allows for implicit con straints to be included. In this article, a description of the Shake-and-Bake algorithm is given, along with a detailed description of master/slave MIMD implemen tations on a network of Sun workstations, an Intel iPSC/860 Hypercube, and a Connection Machine CM-5. Our experimental results on known structures, includ ing gramicidin A, are extremely encouraging. For ex ample, based on efficient implementations of Shake- and-Bake on the iPSC/860 and CM-5, for known struc tures of 28, 84, and 127 nonhydrogen atoms, we obtain success rates of 19%, 1%, and 0.2%, as opposed to existing methods, which yield success rates of ap proximately 6%, 0.006%, and 0.0002%, respectively.