In this paper, parallel algorithms suitable for the iterative solution of large sets of linear equations are developed. The algorithms based on the well known Gauss Seidel and SOR methods are presented in both synchro...
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In this paper, parallel algorithms suitable for the iterative solution of large sets of linear equations are developed. The algorithms based on the well known Gauss Seidel and SOR methods are presented in both synchronous and asynchronous forms. Results obtained using the M.I.M.D. computer at Loughborough University are given, for the model problem of the solution of the Laplace equation within the unit square.
Two current problems in the area of graph theory are the problem of finding a minimal spanning tree (MST) in a connected, weighted, undirected graph and the problem of finding the connected components of an undirected...
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Two current problems in the area of graph theory are the problem of finding a minimal spanning tree (MST) in a connected, weighted, undirected graph and the problem of finding the connected components of an undirected graph. algorithms have been obtained to solve both problems. However, the run time is significantly greater if these algorithms are implemented in a network where read conflicts are not allowed to occur. A new approach is reported which permits the algorithm to run without read conflicts in little more than the time previously required for running in a network where read conflicts were permitted to occur. The new techniques also can be run using a smaller number of processors.
This paper describes two parallel algorithms to test whether a point is inside a digitized closed curve. The first algorithm assumes the curve is stored in a linear array of processors. The second algorithm assumes th...
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This paper describes two parallel algorithms to test whether a point is inside a digitized closed curve. The first algorithm assumes the curve is stored in a linear array of processors. The second algorithm assumes the digital image containing the curve is stored in a 2-D array of processors and that a clockwise (or counterclockwise) trace of the curve is available (i.e., each point on the curve has a pointer to the next clockwise point). Both algorithms assume that scan instructions are available on the processor array. The algorithms take constant numbers of scan instructions.
Methods for the parallel computation of a multidimensional hypercomplex discrete Fourier transform (HDFT) are considered. The basic idea consists in the application of the properties of the hypercomplex algebra in whi...
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Efficient parallel algorithms for computing all possible subset regression models are proposed. The algorithms are based on the dropping columns method that generates a regression tree. The properties of the tree are ...
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Efficient parallel algorithms for computing all possible subset regression models are proposed. The algorithms are based on the dropping columns method that generates a regression tree. The properties of the tree are exploited in order to provide an efficient load balancing which results in no inter-processor communication. Theoretical measures of complexity suggest linear speedup. The parallel algorithms are extended to deal with the general linear and seemingly unrelated regression models. The case where new variables are added to the regression model is also considered. Experimental results on a shared memory machine are presented and analyzed. (C) 2003 Elsevier Science B.V. All rights reserved.
This paper deals with the numerical solution of three-dimensional equilibrium problems in incompressible finite elasticity on parallel computers. The approximation of the underlying variational problems by appropriate...
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This paper deals with the numerical solution of three-dimensional equilibrium problems in incompressible finite elasticity on parallel computers. The approximation of the underlying variational problems by appropriate finite-element methods is discussed and an augmented Lagrangian formulation of the resulting discrete systems is given. Starting from this formulation, a combination of a simple gradient method and a block relaxation process is used to obtain an algorithm for the complicated nonlinear problems, which can be implemented on parallel computers in a very efficient way. Several results of numerical experiments on an array processor illustrate the capabilities of the considered methods.
In this paper, parallel algorithms are presented for solving some problems on permutation graphs. The coloring problem is solved in O(log2n) time using O(n3/log n) processors on the CREW PRAM, or O(log n) time using O...
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In this paper, parallel algorithms are presented for solving some problems on permutation graphs. The coloring problem is solved in O(log2n) time using O(n3/log n) processors on the CREW PRAM, or O(log n) time using O(n3) processors on the CRCW PRAM. The weighted clique problem, the weighted independent set problem, the cliques cover problem, and the maximal layers problem are all solved with the same complexities. We can also show that the longest common subsequence problem belongs to the class NC.
We present a new parallel algorithm for computing a maximum cardinality matching in a bipartite graph suitable for distributed memory computers. The presented algorithm is based on the PUSH-RELABEL. algorithm which is...
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We present a new parallel algorithm for computing a maximum cardinality matching in a bipartite graph suitable for distributed memory computers. The presented algorithm is based on the PUSH-RELABEL. algorithm which is known to be one of the fastest algorithms for the bipartite matching problem. Previous attempts at developing parallel implementations of it have focused on shared memory computers using only a limited number of processors. We first present a straightforward adaptation of these shared memory algorithms to distributed memory computers. However, this is not a viable approach as it requires too much communication. We then develop our new algorithm by modifying the previous approach through a sequence of steps with the main goal being to reduce the amount of communication and to increase load balance. The first goal is achieved by changing the algorithm so that many push and relabel operations can be performed locally between communication rounds and also by selecting augmenting paths that cross processor boundaries infrequently. To achieve good load balance, we limit the speed at which global relabelings traverse the graph. In several experiments on a large number of instances, we study weak and strong scalability of our algorithm using up to 128 processors. The algorithm can also be used to find epsilon-approximate matchings quickly. (C) 2011 Elsevier B.V. All rights reserved.
Two parallel geometric algorithms based on the idea of point domination are presented. The first algorithm solves the d-dimensional isothetic rectangles intersection counting problem of input size N/2(d), where d >...
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Two parallel geometric algorithms based on the idea of point domination are presented. The first algorithm solves the d-dimensional isothetic rectangles intersection counting problem of input size N/2(d), where d > 1 and N is a multiple of 2(d), in O(log(d-1) N) time and O(N log N) space. The second algorithm solves the direct dominance reporting problem for a set of N points in the plane in O(log N + J) time and O(N log N) space, where J denotes the maximum of the number of direct dominances reported by any single point in the set. Both algorithms make use of the EREW PRAM (Exclusive Read Exclusive Write parallel Random Access Machine) consisting of O(N) processors as the computational model.
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