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Results for “Parallel Algorithms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Parallel algorithms for placement and routing in VLSI design

The computational requirements for high quality synthesis, analysis, and verification of very large scale integration (VLSI) designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or parallel algorithms for the numerous design tasks to decrease the time required for solution. Two new parallel algorithms are proposed for two VLSI synthesis tasks, standard cell placement and global routing. The first algorithm, a parallel algorithm for global routing, uses hierarchical techniques to decompose the routing problem into independent routing subproblems that are solved in parallel. Results are then presented which compare the routing quality to the results of other published global routers and which evaluate the speedups attained. The second algorithm, a parallel algorithm for cell placement and global routing, hierarchically integrates a quadrisection placement algorithm, a bisection placement algorithm, and the previous global routing algorithm. Unique partitioning techniques are used to decompose the various stages of the algorithm into independent tasks which can be evaluated in parallel. Finally, results are presented which evaluate the various algorithm alternatives and compare the algorithm performance to other placement programs. Measurements are presented on the parallel speedups available.

Brouwer, Randall Jay↗
NASA NTRS1989

Parallel algorithms and architecture for computation of manipulator forward dynamics

Parallel computation of manipulator forward dynamics is investigated. Considering three classes of algorithms for the solution of the problem, that is, the O(n), the O(n exp 2), and the O(n exp 3) algorithms, parallelism in the problem is analyzed. It is shown that the problem belongs to the class of NC and that the time and processors bounds are of O(log2/2n) and O(n exp 4), respectively. However, the fastest stable parallel algorithms achieve the computation time of O(n) and can be derived by parallelization of the O(n exp 3) serial algorithms. Parallel computation of the O(n exp 3) algorithms requires the development of parallel algorithms for a set of fundamentally different problems, that is, the Newton-Euler formulation, the computation of the inertia matrix, decomposition of the symmetric, positive definite matrix, and the solution of triangular systems. Parallel algorithms for this set of problems are developed which can be efficiently implemented on a unique architecture, a triangular array of n(n+2)/2 processors with a simple nearest-neighbor interconnection. This architecture is particularly suitable for VLSI and WSI implementations. The developed parallel algorithm, compared to the best serial O(n) algorithm, achieves an asymptotic speedup of more than two orders-of-magnitude in the computation the forward dynamics.

Fijany, Amir↗
NASA NTRS1988

Parallel algorithms for mapping pipelined and parallel computations

Many computational problems in image processing, signal processing, and scientific computing are naturally structured for either pipelined or parallel computation. When mapping such problems onto a parallel architecture it is often necessary to aggregate an obvious problem decomposition. Even in this context the general mapping problem is known to be computationally intractable, but recent advances have been made in identifying classes of problems and architectures for which optimal solutions can be found in polynomial time. Among these, the mapping of pipelined or parallel computations onto linear array, shared memory, and host-satellite systems figures prominently. This paper extends that work first by showing how to improve existing serial mapping algorithms. These improvements have significantly lower time and space complexities: in one case a published O(nm sup 3) time algorithm for mapping m modules onto n processors is reduced to an O(nm log m) time complexity, and its space requirements reduced from O(nm sup 2) to O(m). Run time complexity is further reduced with parallel mapping algorithms based on these improvements, which run on the architecture for which they create the mappings.

Nicol, David M.↗
NASA NTRS1988

Parallel algorithm for determining motion vectors in ice floe images by matching edge features

A parallel algorithm is described to determine motion vectors of ice floes using time sequences of images of the Arctic ocean obtained from the Synthetic Aperture Radar (SAR) instrument flown on-board the SEASAT spacecraft. Researchers describe a parallel algorithm which is implemented on the MPP for locating corresponding objects based on their translationally and rotationally invariant features. The algorithm first approximates the edges in the images by polygons or sets of connected straight-line segments. Each such edge structure is then reduced to a seed point. Associated with each seed point are the descriptions (lengths, orientations and sequence numbers) of the lines constituting the corresponding edge structure. A parallel matching algorithm is used to match packed arrays of such descriptions to identify corresponding seed points in the two images. The matching algorithm is designed such that fragmentation and merging of ice floes are taken into account by accepting partial matches. The technique has been demonstrated to work on synthetic test patterns and real image pairs from SEASAT in times ranging from .5 to 0.7 seconds for 128 x 128 images.

Manohar, M.↗
DOE OSTI2020

A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics

This work describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid) and Chombo (Chombo software package for AMR applications—design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202–217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes’ second problem. On a transient Couette flow case, at least a 1.5× speedup is achieved, and with a time periodic problem, a speedup of up to 13.7× over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Massively Parallel Algorithms for Solution of Schrodinger Equation

In this paper massively parallel algorithms for solution of Schrodinger equation are developed. Our results clearly indicate that the Crank-Nicolson method, in addition to its excellent numerical properties, is also highly suitable for massively parallel computation.

parallel algorithms MIMD parallel architectures ti↗
NASA NTRS1992

Optimal parallel algorithms for problems modeled by a family of intervals

A family of intervals on the real line provides a natural model for a vast number of scheduling and VLSI problems. Recently, a number of parallel algorithms to solve a variety of practical problems on such a family of intervals have been proposed in the literature. Computational tools are developed, and it is shown how they can be used for the purpose of devising cost-optimal parallel algorithms for a number of interval-related problems including finding a largest subset of pairwise nonoverlapping intervals, a minimum dominating subset of intervals, along with algorithms to compute the shortest path between a pair of intervals and, based on the shortest path, a parallel algorithm to find the center of the family of intervals. More precisely, with an arbitrary family of n intervals as input, all algorithms run in O(log n) time using O(n) processors in the EREW-PRAM model of computation.

Olariu, Stephan↗
NASA NTRS1989

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Swarztrauber, Paul N.↗
NASA NTRS1990

A parallel algorithm for global routing

A Parallel Hierarchical algorithm for Global Routing (PHIGURE) is presented. The router is based on the work of Burstein and Pelavin, but has many extensions for general global routing and parallel execution. Main features of the algorithm include structured hierarchical decomposition into separate independent tasks which are suitable for parallel execution and adaptive simplex solution for adding feedthroughs and adjusting channel heights for row-based layout. Alternative decomposition methods and the various levels of parallelism available in the algorithm are examined closely. The algorithm is described and results are presented for a shared-memory multiprocessor implementation.

Brouwer, Randall J.↗
DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗
DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

A parallel algorithm for nonlinear convection-diffusion equations

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

Scroggs, Jeffrey S.↗
DOE OSTI2020

Generating Massive Scale-free Networks: Novel Parallel Algorithms using the Preferential Attachment Model

Recently, there has been substantial interest in the study of various random networks as mathematical models of complex systems. As real-life complex systems grow larger, the ability to generate progressively large random networks becomes all the more important. This motivates the need for efficient parallel algorithms for generating such networks. Naïve parallelization of sequential algorithms for generating random networks is inefficient due to inherent dependencies among the edges and the possibility of creating duplicate (parallel) edges. In this article, we present message passing interface-based distributed memory parallel algorithms for generating random scale-free networks using the preferential-attachment model. Our algorithms are experimentally verified to scale very well to a large number of processing elements (PEs), providing near-linear speedups. The algorithms have been exercised with regard to scale and speed to generate scale-free networks with one trillion edges in 6 minutes using 1,000 PEs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Massively Parallel Algorithms for Real-Time Wavefront Control of a Dense Adaptive Optics System

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.

massively↗
NASA NTRS1985

Where are the parallel algorithms?

Four paradigms that can be useful in developing parallel algorithms are discussed. These include computational complexity analysis, changing the order of computation, asynchronous computation, and divide and conquer. Each is illustrated with an example from scientific computation, and it is shown that computational complexity must be used with great care or an inefficient algorithm may be selected.

Voigt, R. G.↗
NASA NTRS1989

Parallel algorithms for computation of the manipulator inertia matrix

The development of an O(log2N) parallel algorithm for the manipulator inertia matrix is presented. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which are required to compute the diagonal elements of the matrix. It results in O(log2N) levels of computation. Computation of the off-diagonal elements involves N linear recurrences of varying-size and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log2N) algorithm is presented in both equation and graphic forms which clearly show the parallelism inherent in the algorithm.

Amin-Javaheri, Masoud↗
NASA NTRS1971

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Stone, H. S.↗