In this work, a new algorithm for drawing a weighted random sample of size m from a population of n weighted items, where m <= n, is presented. The algorithm can generate a weighted random sample in one-pass over u...
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In this work, a new algorithm for drawing a weighted random sample of size m from a population of n weighted items, where m <= n, is presented. The algorithm can generate a weighted random sample in one-pass over unknown populations. (c) 2005 Elsevier B.V. All rights reserved.
In this paper we focus on the problem of designing very fast parallel algorithms for the convex hull and the vector maxima problems in three dimensions that are output-size sensitive. Our algorithms achieve O(log log(...
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In this paper we focus on the problem of designing very fast parallel algorithms for the convex hull and the vector maxima problems in three dimensions that are output-size sensitive. Our algorithms achieve O(log log(2) n log h) parallel time and optimal O(n log h) work with high probability in the CRCW PRAM where n and h are the input and output size, respectively. These bounds are independent of the input distribution and are faster than the previously known algorithms. We also present an optimal speed-up (with respect to the input size only) sublogarithmic time algorithm that uses superlinear number of processors for vector maxima in three dimensions. (C) 2003 Elsevier Science (USA). All rights reserved.
We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for mult...
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We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets.
An earlier suggested parallel "ring" algorithm for solving the spatially onedimensional initial-boundary-value problem (IBVP) for a parabolic equation using an explicit difference method is shortly described...
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An earlier suggested parallel "ring" algorithm for solving the spatially onedimensional initial-boundary-value problem (IBVP) for a parabolic equation using an explicit difference method is shortly described. Theoretical estimates for both of the speed-up function and the communication complexity of this parallel algorithm are studied. The speed-up function is determined as the ratio between times for realization of the algorithm in sequentional and parallel cases. Theoretical estimates of the speed-up function show the significant speed-up of the parallel algorithm in comparison with the serial one for a large number of values computed by one processor during one time level and it is shown that the the speed-up tends to the number of used processors. Communication complexity is determined as a ratio between the number of interchanges and the number of arithmetical operations. It has been proven that the coefficient of the communication complexity for spatially m-dimensional IBVP tends in general to 3/4.
In this paper we present new results on sequential and parallel construction of optimal and almost-optimal length-restricted prefix-free codes. We show that lengthrestricted prefix-free codes with error l/n(k) for any...
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In this paper we present new results on sequential and parallel construction of optimal and almost-optimal length-restricted prefix-free codes. We show that lengthrestricted prefix-free codes with error l/n(k) for any k > 0 can be constructed in O(n log n) time, or in O(logn) time with n CREW processors. A length-restricted code with error l/n(k) for any k <= L/log(Phi)n, where Phi = (1 + root 5)/2, can be constructed in O(logn) time with n/log n CREW processors. We also describe an algorithm for the construction of optimal length-restricted codes with maximum codeword length L that works in O(L) time with n CREW processors.
Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has Lis a main c...
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Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has Lis a main component the Generalized QR decomposition. The proposed algorithm is based on orthogonal transformations and exploits the triangular structure of the Cholesky QRD factor of the variance-covariance matrix. Specifically, it computes the estimator of the general linear model by solving recursively a series of smaller and smaller generalized linear least squares problems. The new algorithm is found to Outperform significantly the corresponding LAPACK routine. A parallel version of the new sequential algorithm which utilizes an efficient distribution of the matrices over the processors and has low inter-processor communication is developed. The theoretical computational complexity of the parallel algorithms is derived and analyzed. Experimental results are presented which confirm the theoretical analysis. The parallel strategy is found to be scalable and highly efficient for estimating large-scale general linear estimation problems. (c) 2005 Elsevier B.V. All rights reserved.
This paper develops locally adapted hierarchical basis functions for effectively preconditioning large optimization problems that arise in computer graphics applications such as tone mapping, gradient-domain blending,...
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This paper develops locally adapted hierarchical basis functions for effectively preconditioning large optimization problems that arise in computer graphics applications such as tone mapping, gradient-domain blending, colorization, and scattered data interpolation. By looking at the local structure of the coefficient matrix and performing a recursive set of variable eliminations, combined with a simplification of the resulting coarse level problems, we obtain bases better suited for problems with inhomogeneous ( spatially varying) data, smoothness, and boundary constraints. Our approach removes the need to heuristically adjust the optimal number of preconditioning levels, significantly outperforms previously proposed approaches, and also maps cleanly onto data-parallel architectures such as modern GPUs.
We analyze the spatial smoothing algorithm of Solis, Borkar and Kumar [1] for clock synchronization over multi-hop wireless networks. In particular, for a model of a random wireless network we show that with high prob...
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ISBN:
(纸本)9781424401703
We analyze the spatial smoothing algorithm of Solis, Borkar and Kumar [1] for clock synchronization over multi-hop wireless networks. In particular, for a model of a random wireless network we show that with high probability the error variance is O(1) as the number of nodes in the network increases. This provides support for the feasibility of time-based computing n large wireless networks. We also provide bounds on the settling time of a distributed algorithm.
We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number ...
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ISBN:
(纸本)3540446249
We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number of rounds in the message passing model and the approximation error can be made O(1/log(k) vertical bar G vertical bar) where vertical bar G vertical bar is the order of the graph and k is a positive integer.
Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has Lis a main c...
详细信息
Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has Lis a main component the Generalized QR decomposition. The proposed algorithm is based on orthogonal transformations and exploits the triangular structure of the Cholesky QRD factor of the variance-covariance matrix. Specifically, it computes the estimator of the general linear model by solving recursively a series of smaller and smaller generalized linear least squares problems. The new algorithm is found to Outperform significantly the corresponding LAPACK routine. A parallel version of the new sequential algorithm which utilizes an efficient distribution of the matrices over the processors and has low inter-processor communication is developed. The theoretical computational complexity of the parallel algorithms is derived and analyzed. Experimental results are presented which confirm the theoretical analysis. The parallel strategy is found to be scalable and highly efficient for estimating large-scale general linear estimation problems. (c) 2005 Elsevier B.V. All rights reserved.
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