This paper discusses the possibilities for parallel processing of the Full- and Limited-Memory BFGS training algorithms, two powerful second-order optimization techniques used to train Multilayer Perceptrons. The step...
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This paper discusses the possibilities for parallel processing of the Full- and Limited-Memory BFGS training algorithms, two powerful second-order optimization techniques used to train Multilayer Perceptrons. The step size and gradient calculations are identified as the critical components in both. The matrix calculations in the Full-Memory algorithm are also shown to be significant for larger problems. Various strategies are considered for parallelisation, the best of which is implemented on PVM and transputer based architectures. The generation of a neural predictive model for a nonlinear chemical plant is used as a control case study to assess parallel performance in terms of achievable speed-up. The transputer implementation is found to give excellent speed-ups but the size of problem that can be trained is limited by memory constraints. On the other hand speed-ups achievable with the PVM implementation are much poorer because of inefficient communication, but memory does not pose a problem.
The rational and suitability of implementing model fitting algorithms on vector and parallel computers are discussed. A particular maximum likelihood based algorithm for fitting of two-dimensional "Gaussian"...
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The rational and suitability of implementing model fitting algorithms on vector and parallel computers are discussed. A particular maximum likelihood based algorithm for fitting of two-dimensional "Gaussian" peaks was investigated in detail and adapted to a system of four transputers. Analysis of the algorithm shows it well suited to both vectorisation and parallelisation;this result being applicable to other fitting methods. The transputer implementation gave an increase in performance (5-10 times faster) compared to the host computer, allowing the model fitting procedure to approach acceptable response times.
Interval orders are partial orders defined by having interval representations. It is well known that a transitively oriented digraphGis an interval order iff its (undirected) complement G¯ is chordal. We investig...
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Interval orders are partial orders defined by having interval representations. It is well known that a transitively oriented digraphGis an interval order iff its (undirected) complement G¯ is chordal. We investigate parallel algorithms Tot the following scheduling problem: Given a system consisting of a setTofntasks (each requiring unit execution time) and an interval order ≺ overT, and given m identical parallel processors, construct an optimal (i.e., minimal length) schedule for (T, ≺).Our algorithm is based on a subroutine for computing so-called scheduling distances, i.e., the minimal number of time steps needed to schedule all those tasks succeeding some given tasktand preceding some other taskt1. For a given interval order with n tasks, these scheduling distances can be computed usingn3processors andO(log2n) time on a CREW-PRAM. We then give an incremental version of the scheduling distance algorithm, which can be used to compute the empty slots in an optimal schedule. From these, we derive the optimal schedule, using no more resources than for the initial scheduling distance computation and considerably improving on previous work by Sunder and *** algorithm can also be extended to handle task systems which, in addition to interval order precedence constraints, have individual deadlines and/or release times for the tasks. Our algorithm is the firstNC-algorithm for this problem. As another application, it also providesNC-algorithms for some graph problems on interval graphs (which areNP-complete in general).
A preconditioned Krylov iterative algorithm based on domain decomposition for linear systems arising from implicit finite-difference or finite-element discretizations of partial differential equation problems requirin...
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A preconditioned Krylov iterative algorithm based on domain decomposition for linear systems arising from implicit finite-difference or finite-element discretizations of partial differential equation problems requiring local mesh refinement is described. To keep data structures as simple as possible for parallel computing applications, the fundamental computational unit in the algorithm is defined as a subregion of the domain spanned by a locally uniform tensor-product grid, called a tile. In the tile-based domain decomposition approach, two levels of discretization are considered at each point of the domain: a global coarse grid defined by tile vertices only, and a local fine grid where the degree of resolution can vary from tile to tile. One global level and one local level provide the flexibility required to adaptively discretize a diverse collection of problems on irregular regions and solve them at convergence rates that deteriorate only logarithmically in the finest mesh parameter, with the coarse tessellation held fixed. A logarithmic departure from optimality seems to be a reasonable compromise for the simplicity of the composite grid data structure and concomitant regular data exchange patterns in a multiprocessor environment. Some experiments with up to 1024 tiles are reported, and the evolution of the algorithm is commented on and contrasted with optimal nonrefining two-level algorithms and optimal refining multilevel algorithms. Computational comparisons with some other popular methods are presented.
The performance of hash tables is analyzed in a parallel context. Assuming that a hash table of fixed size is allocated in the shared memory of a PRAM with n processors, a Ph-step is defined as a PRAM computation in w...
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The performance of hash tables is analyzed in a parallel context. Assuming that a hash table of fixed size is allocated in the shared memory of a PRAM with n processors, a Ph-step is defined as a PRAM computation in which each processor searches or inserts a key in the table. It is shown that the maximum number of table probes needed for a single key in a Ph-step is Ω( log 1/α n ) and O( log 1/α′ n ) with high probability, where α and α′ are the load factors before and after the execution of the Ph-step. However, a clever implementation of a Ph-step is proposed, which runs in time O(( log 1/α′ n) 1/2 ) with high probability. The algorithm exploits the fact that operations relative to different keys have different durations; hence, the processors in charge of shorter operations, once finished, are used to perform part of the longer ones.
This paper presents a complete and optimal framework for extending basic graph planning to operate in partitioned problem spaces. These spaces typically occur in systems that implement a hierarchy or contain data of v...
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This paper presents a complete and optimal framework for extending basic graph planning to operate in partitioned problem spaces. These spaces typically occur in systems that implement a hierarchy or contain data of various resolutions. An algorithm for the framework will be presented along with a proof of optimality. Finally, an example implementation for mobile robot path planning will be discussed.
The solutions to a scalar, homogeneous, constant-coefficient, linear recurrence are expressible in terms of the powers of a companion matrix. We show how to compute these powers efficiently via polynomial multiplicati...
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The solutions to a scalar, homogeneous, constant-coefficient, linear recurrence are expressible in terms of the powers of a companion matrix. We show how to compute these powers efficiently via polynomial multiplication. The result is a simple expression for the solution, which does not involve the characteristic roots and which is valid for any module over any commutative ring. The formula yields the nth term of the solution to a kth order recurrence with O(μ(k)
In this paper, we present an efficient parallel algorithm for computing the visibility region for a point in a plane among a non-intersecting set of segments. The algorithm is based on the cascading divide-and-conquer...
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In this paper, we present an efficient parallel algorithm for computing the visibility region for a point in a plane among a non-intersecting set of segments. The algorithm is based on the cascading divide-and-conquer technique and uses merge path to evenly distribute the workload between processors. We implemented the algorithm on NVIDIA's CUDA platform where it performed with a speedup up to 76x with respect to the serial CPU version.
Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be e...
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Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of scattering problems discretized with hundreds of millions of unknowns by employing a parallel implementation of the Multilevel Fast Multipole Algorithm. Various examples involving canonical and complicated objects, including scatterers larger than 1000 lambda, are presented, in order to demonstrate the feasibility of accurately solving large-scale problems on relatively inexpensive computing platforms.
A tabu search based approach is studied as a method for solving in parallel the two-dimensional irregular cutting problem. We use and compare different, variants of the method and various parallel computing systems. S...
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A tabu search based approach is studied as a method for solving in parallel the two-dimensional irregular cutting problem. We use and compare different, variants of the method and various parallel computing systems. Systems used are based on message passing or shared memory paradigm. parallel algorithms using both methods of communication are proposed. The efficiency of computer system utilization is discussed in the context of unpredictable time requirements of parallel tasks. We present results for different variants of the method together with efficiency measures for parallel implementations, where IBM SP2 and CRAY T3E systems, respectively, have been used.
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