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Out-of-core computing on mesh connected computers

JOURNAL OF PARALLEL AND DISTRIBUTED computing 2004年第11期64卷 1311-1317页

作者： Rajasekaran, S Univ Connecticut Dept CSE Storrs CT 06269 USA

Several models of parallel disks are found in the literature. These models have been proposed to alleviate the I/O bottleneck arising in handling voluminous data. These models have the general theme of assuming multiple disks. For instance the parallel disks model assumes D disks and a single computer. It is also assumed that a block of data from each of the D disks can be fetched into the main memory in one parallel I/O operation. In this paper, we study a model where there are more than one processors and each processor has an associated disk. In addition to the I/O cost, one also has to account for the inter-processor communication costs. To begin with we study the mesh and we investigate the performance of the mesh with respect to out-of-core computing. As a case study we consider the problem of sorting. The goal of this paper is to study the properties of this model. (C) 2004 Elsevier Inc. All rights reserved.

关键词： out-of-core computing I/O bottleneck parallel models of computing mesh connected computers parallel disks model sorting algorithms packet routing randomized computing

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On the complexity of a two-point boundary value problem in different settings

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010年第15期87卷 3370-3386页

作者： Gocwin, Maciej Szczesny, Marek AGH Univ Sci & Technol Fac Appl Math PL-30059 Krakow Poland

We study the complexity of a two-point boundary value problem. We concentrate on the linear problem of order k with separated boundary conditions. Right-hand side functions are assumed to be r times differentiable with all derivatives bounded by a constant. We consider three models of computation: deterministic with standard and linear information, randomized and quantum. In each setting, we construct an algorithm for solving the problem, which allows us to establish upper complexity bounds. In the deterministic setting, we show that the use of linear information gives us a speed-up of at least one order of magnitude compared with the standard information. For randomized algorithms, we show that the speed-up over standard deterministic algorithms is by 1/2 in the exponent. For quantum algorithms, we can achieve a speed-up by one order of magnitude. We also provide lower complexity bounds. They match upper bounds in the deterministic setting with the standard information, and almost match upper bounds in the randomized and quantum settings. In the deterministic setting with the linear information, a gap still remains between the upper and lower complexity bounds.

关键词： boundary value problems complexity worst-case setting randomized computing quantum computing

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randomized and quantum complexity of nonlinear two-point BVPs

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APPLIED MATHEMATICS AND COMPUTATION 2014年第0期245卷 357-371页

作者： Gocwin, Maciej AGH Univ Sci & Technol Fac Appl Math PL-30059 Krakow Poland

We deal with the complexity of nonlinear BVPs with nonlinear two-point boundary conditions. We consider the randomized and quantum models of computation. We assume that the right-hand side function is r times differentiable with all derivatives bounded by a constant. We show that the epsilon-complexity is roughly of order epsilon(-1/(r+1/2)) in the randomized setting, and epsilon(-1/(r+1)) in the quantum setting. We compare our results with known results in the deterministic setting. The speed-up of the randomized computations with respect to the deterministic computations is by 1/(r(2r + 1)) in the exponent of 1/epsilon, and the speed-up of the quantum computations by 1/(r(r +1)) in the exponent. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Boundary value problems Complexity Optimal algorithms randomized computing Quantum computing

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Complexity measures and decision tree complexity: a survey

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THEORETICAL COMPUTER SCIENCE 2002年第1期288卷 21-43页

作者： Buhrman, H de Wolf, R CWI NL-1098 SJ Amsterdam Netherlands Univ Amsterdam ILLC NL-1018 TV Amsterdam Netherlands

We discuss several complexity measures for Boolean functions: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： decision tree complexity complexity measures for Boolean functions randomized computing quantum computing

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Mit :: Lcs :: Tr :: Mit-Lcs-Tr-651

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2016年

Mit :: Lcs :: Tr :: Mit-Lcs-Tr-651 by published by

关键词： adversary algorithm chapter execution general model lemma mit-lcs-tr-651 mutual exclusion optimal randomized player probability probability distribution probability space random random variable random variables randomized randomized algorithm randomized algorithms randomized computing set

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