Showing papers on "Computation published in 1993"

LogP: towards a realistic model of parallel computation

Abstract: A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding development of techniques that yield performance across a range of current and future parallel machines. This paper offers a new parallel machine model, called LogP, that reflects the critical technology trends underlying parallel computers. it is intended to serve as a basis for developing fast, portable parallel algorithms and to offer guidelines to machine designers. Such a model must strike a balance between detail and simplicity in order to reveal important bottlenecks without making analysis of interesting problems intractable. The model is based on four parameters that specify abstractly the computing bandwidth, the communication bandwidth, the communication delay, and the efficiency of coupling communication and computation. Portable parallel algorithms typically adapt to the machine configuration, in terms of these parameters. The utility of the model is demonstrated through examples that are implemented on the CM-5.

FastHenry: A Multipole-Accelerated 3-D Inductance Extraction Program

Abstract: In [1], it was shown that an equation formulation based on mesh analysis can be combined with a GMRES-style iterative matrix solution technique to make a reasonably fast 3-D frequency dependent inductance and resistance extraction algorithm. Unfortunately, both the computation time and memory required for that approach grow faster than n/sup 2/, where n is the number of volume-filaments. In this paper, we show that it is possible to use multipole-acceleration to reduce both required memory and computation time to nearly order n. Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic packaging problems.

Towards a Mathematical Science of Computation

Abstract: In this paper I shall discuss the prospects for a mathematical science of computation. In a mathematical science, it is possible to deduce from the basic assumptions, the important properties of the entities treated by the science. Thus, from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler’s laws.

Interactive computation of holograms using a look-up table

Abstract: Several methods of increasing the speed and simplicity of the computation of off-axis transmission holograms are presented, with applications to the real-time display ofholographic images. The bipolar intensity approach allows for the real-valued linear summation of interference fringes, a factor of 2 speed increase, and the elimination of image noise caused by object self-interference. An order of magnitude speed increase is obtained through the use of a precomputed look-up table containing a large array of elemental interference patterns corresponding to point source contributions from each of the possible locations in image space. Results achieved using a data-parallelsupercomputer to compute horizontal-parallaxonly holographic patterns containing six megasamples indicate that an image comprised of 10,000 points with arbitrary brightness (gray scale) can be computed in under 1 s. Implemented on a common workstation, the look-up table approach increases computation speed by a factor of 43.

Interpolation by regularized spline with tension. II: Application to terrain modeling and surface geometry analysis

Abstract: A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfill the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.

Boundary conditions for direct computation of aerodynamic sound generation

Abstract: A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

Efficient collision detection for animation and robotics

Abstract: We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between $O(\sqrt{n})$ and O(n) depending on the shape, if no special initialization is done. This technique can be used for dynamic collision detection, planning in three-dimensional space, physical simulation, and other robotics problems. The set of models we consider includes polyhedra and objects with surfaces described by rational spline patches or piecewise algebraic functions. We use the expected constant time distance computation algorithm for collision detection between convex polyhedral objects and extend it using a hierarchical representation to distance measurement between non-convex polytopes. Next, we use global algebraic methods for solving polynomial equations and the hierarchical description to devise efficient algorithms for arbitrary curved objects. We also describe two different approaches to reduce the frequency of collision detection from$$N\choose2$$pairwise comparisons in an environment with n moving objects. One of them is to use a priority queue sorted by a lower bound on time to collision; the other uses an overlap test on bounding boxes. Finally, we present an opportunistic global path planner algorithm which uses the incremental distance computation algorithm to trace out a one-dimensional skeleton for the purpose of robot motion planning. The performance of the distance computation and collision detection algorithms attests their promise for real-time dynamic simulations as well as applications in a computer generated virtual environment.

Mixture models for optical flow computation

Abstract: The computation of optical flow relies on merging information available over an image patch to form an estimate of 2-D image velocity at a point. This merging process raises many issues. These include the treatment of outliers in component velocity measurements and the modeling of multiple motions within a patch which arise from occlusion boundaries or transparency. A new approach for dealing with these issues is presented. It is based on the use of a probabilistic mixture model to explicitly represent multiple motions within a patch. A simple extension of the EM-algorithm is used to compute a maximum likelihood estimate for the various motion parameters. Preliminary experiments indicate that this approach is computationally efficient, and that it can provide robust estimates of the optical flow values in the presence of outliers and multiple motions. >

Parallel finite-element computation of 3D flows

Abstract: The authors describe their work on the massively parallel finite-element computation of compressible and incompressible flows with the CM-200 and CM-5 Connection Machines. Their computations are based on implicit methods, and their parallel implementations are based on the assumption that the mesh is unstructured. Computations for flow problems involving moving boundaries and interfaces are achieved by using the deformable-spatial-domain/stabilized-space-time method. Using special mesh update schemes, the frequency of remeshing is minimized to reduce the projection errors involved and also to make parallelizing the computations easier. This method and its implementation on massively parallel supercomputers provide a capability for solving a large class of practical problems involving free surfaces, two-liquid interfaces, and fluid-structure interactions. >

Distributed estimation and quantization

Abstract: An algorithm is developed for the design of a nonlinear, n-sensor, distributed estimation system subject to communication and computation constraints. The algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints. It is shown that the algorithm is a generalization of the classical Lloyd-Max results. >

Improved strategy in analytic surface calculation for molecular systems: handling of singularities and computational efficiency

Abstract: Computer methods for analytic surface calculations of molecular systems suffer from numerical instabilities and are CPU time consuming. In this article, we present proposals toward the solution of both problems. Singularities arise when nearly collinear triples of neighboring atoms or multiple vertices are encountered during the calculation. Topological decisions in analytic surface calculation algorithms (accessibility of vertices and arcs) are based upon the comparison of distances or angles. If two such numbers are nearly equal, then currently used computer programs may not resolve this ambiguity correctly and can subsequently fail. In this article, modifications in the analytic surface calculation algorithm are described that recognize singularities automatically and treat them appropriately without restarting parts of the computation. The computing time required to execute these alterations is minimal. The basic modification consists in defining an accuracy limit within which two values may be assumed as equal. The search algorithm has been reformulated to reduce the computational effort. A new set of formulas makes it possible to avoid mostly the extraction of square roots. Tests for small-and medium-sized intersection circles and for pairs of vertices with small vertex height help recognize fully buried circles and vertex pairs at an early stage. The new program can compute the complete topology of the surface and accessible surface area of the protein crambin in 1.50–4.29 s (on a single R3000 processor of an SGI 4D/480) depending on the compactness of the conformation where the limits correspond to the fully extended or fully folded chain, respectively. The algorithm, implemented in a computer program, will be made available on request. © John Wiley & Sons, Inc.

Randomized parallel algorithms for backtrack search and branch-and-bound computation

Abstract: Universal randomized methods for parallelizing sequential backtrack search and branch-and-bound computation are presented. These methods execute on message-passing multi- processor systems, and require no global data structures or complex communication protocols. For backtrack search, it is shown that, uniformly on all instances, the method described in this paper is likely to yield a speed-up within a small constant factor from optimal, when all solutions to the problem instance are required. For branch-and-bound computation, it is shown that, uniformly on all instances, the execution time of this method is unlikely to exceed a certain inherent lower bound by more than a constant factor. These randomized methods demonstrate the effectiveness of randomization in distributed parallel computation. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity): Non-numerical Algorithms-computation

Vector quantization for the efficient computation of continuous density likelihoods

Abstract: In speech recognition systems based on continuous observation density hidden Markov models, the computation of the state likelihoods is an intensive task. The author presents an efficient method for the computation of the likelihoods defined by weighted sums (mixtures) of Gaussians. This method uses vector quantization of the input feature vector to identify a subset of Gaussian neighbors. It is shown that, under certain conditions, instead of computing the likelihoods of all the Gaussians, one needs to compute the likelihoods of only the Gaussian neighbours. Significant (up to a factor of nine) likelihood computation reductions have been obtained on various data bases, with only a small loss of recognition accuracy. >

Computation of mean-semivariance efficient sets by the Critical Line Algorithm

Abstract: The general mean-semivariance portfolio optimization problem seeks to determine the efficient frontier by solving a parametric non-quadratic programming problem. In this paper it is shown how to transform this problem into a general mean-variance optimization problem, hence the Critical Line Algorithm is applicable. This paper also discusses how to implement the critical line algorithm to save storage and reduce execution time.

A categorized bibliography on incremental computation

Abstract: In many kinds of emnputatiomd contexts, modifications of the input data are to be processed at once so as to have immediate effect on the output. Because small changes in the input to a computation often cause only small changes in the outpu~ the challenge is to compute the new output incrementally by updating parts of the old outpu~ rather than by recomputing the entire output from scratch (as a “batch computation”)

A Robust Image Reconstruction Algorithm and Its Parallel Implementation in

Abstract: We have developed an efficient and robust im- age reconstruction algorithm for static impedance imaging us- ing Hachtel's augmented matrix method. This improved New- ton-Raphson method produced more accurate images by reduc- ing the undesirable effects of the ill-conditioned Hessian matrix. We demonstrated that our electrical impedance tomography (EIT) system could produce two-dimensional static images from a physical phantom with 7 percent spatial resolution at the center and 5 percent at the periphery. Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations on reducing the computation time by algorithmic approaches, we implemented the improved Newton-Raphson algorithm on a parallel computer system and showed that the parallel computation could reduce the computation time from hours to minutes.

Modeling error sources in digital channels

Abstract: A modified Baum-Welch algorithm is developed and applied to estimating parameters of error source models that belong to the class of hidden Markov models (HMM). Such models arise in the description of bursty error statistics in communication channels. A key element used repeatedly for estimating parameters of such models is the computation of the likelihood of given sequences of observations. Several recursive methods are available for efficiently computing this likelihood. However, even recursive methods can require prohibitive amounts of computation if the observation sequences are very long. Modifications of the Baum-Welch reestimation algorithm that significantly reduces the computational requirements when the observation sequences contain long stretches of identical observations are discussed. The algorithms are used here to estimate parameters of a binary error source model using the results of computer simulation. >

A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography

Abstract: An efficient and robust image reconstruction algorithm for static impedance imaging using Hachtel's augmented matrix method was developed. This improved Newton-Raphson method produced more accurate images by reducing the undesirable effects of the ill-conditioned Hessian matrix. It is demonstrated that the electrical impedance tomography (EIT) system could produce two-dimensional static images from a physical phantom with 7% spatial resolution at the center and 5% at the periphery. Static EIT image reconstruction requires a large amount of computation. In order to overcome the limitations on reducing the computation time by algorithmic approaches, the improved Newton-Raphson algorithm was implemented on a parallel computer system. It is shown that the parallel computation could reduce the computation time from hours to minutes. >

Computation of isotropic tensor functions

Abstract: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented

Path computation algorithms for advanced traveller information system (ATIS)

Abstract: Three path-planning algorithms for single-pair path computation are evaluated. These algorithms are the iterative breath-first search, Dijkstra's single-source path-planning algorithm, and the A* single-path planning algorithm. The performance of the algorithms is evaluated on graphs representing the roadmap of Minneapolis. In order to get an insight into their relative performance, synthetic grid maps are used as a benchmark computation. The effects of two parameters, namely path length and edge-cost-distribution, on the performance of the algorithms are examined. The effects of implementation decisions on the performance of the A* algorithm are discussed. The main hypothesis is that estimator functions can improve the average-case performance of single-pair path computation when the length of the path is small compared to the diameter of the graph. This hypothesis is examined using experimental studies and analytical cost modeling. >

Robust computation of optical flow in a multi-scale differential framework

Abstract: The authors developed an algorithm for computing optical flow in a differential framework. The image sequence is first convolved with a set of linear, separable spatiotemporal filters similar to those that have been used in other early vision. The brightness constancy constraint can then be applied to each of the resulting images, giving in general, an overdetermined system of equations for the optical flow at each pixel. There are three principal sources of error: (a) stochastic due to sensor noise, (b) systematic errors in the presence of large displacements, and (c) errors due to failure of the brightness constancy model. The analysis of these errors leads to development of an algorithm based on a robust version of total least squares. Each optical flow vector computed has an associated reliability measure which can be used in subsequent processing. The performance of the algorithm on the data set used by J. Barron et al. (1992) compares favorably with other techniques. In addition to being separable, the filters used are also causal, incorporating only past time frames. The algorithm is fully parallel and has been implemented on a multipleprocessor machine. >

The Order of Computation for Finite Discrete Gabor Transforms

Abstract: Equations for the continuous-parameter Gabor transform are presented and converted to finite discrete form suitable for digital computation. A comparative assessment of the computational complexity of several algorithms that execute the finite discrete equations is given, with results in the range O ( P 2 ) to O ( P log, P), where P is the number of input data points being transformed. The most efficient of the reviewed methods, which uses the Zak transform as an operational calculus, performs Gabor analysis and synthesis transforms with complexity of the same order as a fast Fourier transform (FFT).

A Parallel Build-up Algorithm for Global Energy Minimizations of Molecular Clusters Using Effective Energy Simulated Annealing

Abstract: This work studies the build-up method for the global minimization problem for molecular conformation, especially protein folding. The problem is hard to solve for large molecules using general minimization approaches because of the enormous amount of required computation. We therefore propose a build-up process to systematically "construct" the optimal molecular structures. A prototype algorithm is designed using the anisotropic effective energy simulated annealing method at each build-up stage. The algorithm has been implemented on the Intel iPSC/860 parallel computer, and tested with the Lennard-Jones microcluster conformation problem. The experiments showed that the algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation. In particular, for the 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.