Control algorithms for accurate and fast moving robots require computations based on the complete dynamic model of the robot. These computations are time consuming due to the high degree of coupling between robot link...
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Control algorithms for accurate and fast moving robots require computations based on the complete dynamic model of the robot. These computations are time consuming due to the high degree of coupling between robot links and the nonlinear dependence of the robot's dynamic characteristics on orientation of the links. A method for processing the dynamic control equations in real-time by using parallel computation is described. The recursive Newton-Euler equations are distributed over multiple computing elements, one for each joint. Concurrency is achieved by substituting "predicted" values for the actual values of variables involved in the recursive equations. The method has been simulated and compared to other approaches to this problem such as simplification of the dynamic equations. The experimental results have shown that the errors introduced by prediction are relatively small and compare very favorably to other techniques. The computer architecture and algorithms presented offer a practical way to implement the control algorithms with relatively inexpensive computing devices.
We discuss parallel algorithms for solving eight common standard and generalized triangular Sylvester-type matrix equation. Our parallel algorithms are based on explicit blocking, 2D block-cyclic data distribution of ...
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Floorplan design is the first task in VLSI layout and perhaps the most important one. It is the problem of allocating space to a set of modules in the plane in order to minimize the area of the bounding rectangle. The...
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An edge is a bisector of a simple path if it contains the middle point of the path. Let T = (V, E) be a tree. Given a source vertex s is an element of V, the single-source tree bisector problem is to find, for every v...
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An edge is a bisector of a simple path if it contains the middle point of the path. Let T = (V, E) be a tree. Given a source vertex s is an element of V, the single-source tree bisector problem is to find, for every vertex v is an element of V, a bisector of the simple path from s to v. The all-pairs tree bisector problem is to find for, every pair of vertices u, v is an element of V, a bisector of the simple path from u to v. In this paper, it is first shown that solving the single-source tree bisector problem of a weighted tree has a time lower bound Omega (n log n) in the sequential case. Then, efficient parallel algorithms are proposed on the EREW PRAM for the single-source and all-pairs tree bisector problems. Two O(log n) time single-source algorithms are proposed. One uses O(n) work and is for unweighted trees. The other uses O(n log n) work and is for weighted trees. Previous algorithms for the single-source problem could achieve the same time O(log n) and the same optimal work, O(n) for unweighted trees and O(n log n) for weighted trees, on the CRCW PRAM. The contribution of our single-source algorithms is the improvement from CRCW to EREW. One all-pairs parallel algorithm is proposed. It requires O(log n) time using O(n(2)) work. All the proposed algorithms are cost-optimal. Efficient tree bisector algorithms have practical applications to several location problems on trees. Using the proposed algorithms, efficient parallel solutions for those problems are also presented.
In this paper: we present rounding error bounds of recent parallel versions of Forsythe's and Clenshaw's algorithms for the evaluation of finite series uf Chebyshev polynomials of the first and second kind. Th...
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In this paper: we present rounding error bounds of recent parallel versions of Forsythe's and Clenshaw's algorithms for the evaluation of finite series uf Chebyshev polynomials of the first and second kind. The backward errors are studied by using the matrix formulation of the algorithm, whereas the forward error is also Studied by means of a more direct approach that permits us to obtain sharper bounds. The bounds show all almost stable behavior as ill the sequential algorithms. This fact is: illustrated with several numerical tests. (C) 2001 Elsevier Science Ltd. All rights reserved.
We study parallel algorithms for lossless data compression via textual substitution. Dynamic dictionary compression is known to be P - complete, however, if the dictionary is given in advance, we show that compression...
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To verify whether a spanning tree T(V,E) of graph G(V,E′) is a minimum spanning tree, two parallel algorithms are presented in this paper. The first algorithm requires O(logn) time and O(max{m/logn, n3/2/logn}) proce...
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To verify whether a spanning tree T(V,E) of graph G(V,E′) is a minimum spanning tree, two parallel algorithms are presented in this paper. The first algorithm requires O(logn) time and O(max{m/logn, n3/2/logn}) processors, where |E′|=m and |V|=n. The second algorithm requires O(logn) time and O(m) processors or O(lognloglogn) time and O(max{m/logn, n}) processors. The first algorithm is optimal when G is dense, compared with its O(m) time sequential version. The second algorithm has better performance when G is sparse. By using above results, we also present an efficient algorithm for sensitivity analysis of minimum spanning trees which requires O(logn) time and O(max{m, n2/logn}) processors. All proposed algorithms in this paper are based on the parallel computational model called CREW PRAM.
parallel updates of minimum spanning trees (MSTs) have been studied in the past, These updates allowed a single change in the underlying graph, such as a change in the cost of an edge or an insertion of a new vertex. ...
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parallel updates of minimum spanning trees (MSTs) have been studied in the past, These updates allowed a single change in the underlying graph, such as a change in the cost of an edge or an insertion of a new vertex. Multiple update problems for MSTs are concerned with handling more than one such change. In the sequential case multiple update problems may be solved using repeated applications of an efficient algorithm for a single update. However, for efficiency reasons, parallel algorithms for multiple update problems must consider all changes to the underlying graph simultaneously. In this paper we describe parallel algorithms for updating an MST when k new vertices are inserted or deleted in the underlying graph, when the costs of k edges are changed, or when k edge insertions and deletions are performed. For multiple vertex insertion update, our algorithm achieves time and processor bounds of O(log n . log k) and nk/(log n . log k), respectively, on a CREW parallel random access machine. These bounds are optimal for dense graphs. A novel feature of this algorithm is a transformation of the previous MST and k new vertices to a bipartite graph which enables us to obtain the above-mentioned bounds.
This paper describes a methodology for the implementation of asynchronous parallel algorithms on multicomputer systems. The algorithms studied here belong to the class of iterative methods. The proposed methodology is...
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This paper describes a methodology for the implementation of asynchronous parallel algorithms on multicomputer systems. The algorithms studied here belong to the class of iterative methods. The proposed methodology is based on the definition of a computational model by which an algorithm is specified as a set of concurrent processes mapped onto a set of processors and communicating by asynchronous message passing. This approach can be appealing and innovative since there is a need to reduce the cost of synchronization that affects synchronous algorithms. As an application of the proposed approach, the implementation on a network of INMOS Transputers of an asynchronous parallel version of the classical Newton method for solving nonlinear optimization problems is described and discussed. In this implementation each computational task of the algorithm is implemented as an Occam process running on a Transputer. The performance results of the numerical experiments are encouraging and show the effectiveness of the proposed approach.
A new alternating group explicit method for solving convection dominated diffusion problem of variable coefficient is presented, and the energy method is used to prove the stability of the method.
A new alternating group explicit method for solving convection dominated diffusion problem of variable coefficient is presented, and the energy method is used to prove the stability of the method.
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