The development of mathematical programming algorithms and heuristics has traditionally been hampered by the separation of modeller and optimiser. Developers either have to sacrifice performance by switching between a...
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The development of mathematical programming algorithms and heuristics has traditionally been hampered by the separation of modeller and optimiser. Developers either have to sacrifice performance by switching between a modeller and optimiser and communicating through cumbersome matrix files;or they can work solely with the in-core matrix in the optimiser, where knowledge about the structured algebraic model is missing and thus difficult to exploit. We present EMOSL, a new combined modelling and optimisation subroutine library that overcomes these drawbacks. It allows the problem to be manipulated using the notation of the model language, which is of course close to the algebraic formulation of the problem. Access is provided directly to the in-core matrix of the optimiser, eliminating the need to communicate via files. Thus the scope and ease of algorithm development is greatly improved, without any degradation of performance. We substantiate these claims by describing four applications: a block structure extraction tool, and the implementations of three MIP heuristics and cutting planes techniques.
A least-squares based method for noisy autoregressive signals has been developed recently, which needs to neither prefilter noisy data nor perform parameter extraction. In this brief, a more computationally efficient ...
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A least-squares based method for noisy autoregressive signals has been developed recently, which needs to neither prefilter noisy data nor perform parameter extraction. In this brief, a more computationally efficient procedure for estimating the measurement noise variance is developed, and then an efficient implementation of the method is presented. It is shown that this better way of implementation can considerably reduce the computational requirement of the least-squares based method without any performance degradation. Computer simulations that support the theoretical findings are given.
This article defines input perturbations so that an algorithm designed under certain restrictions on the input can execute on arbitrary instances. A syntactic definition of perturbations is proposed and certain proper...
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This article defines input perturbations so that an algorithm designed under certain restrictions on the input can execute on arbitrary instances. A syntactic definition of perturbations is proposed and certain properties are specified under which an algorithm executed on perturbed input produces an output from which the exact answer can be recovered. A general framework is adopted for linear perturbations, which are efficient from the point of view of worst-case complexity. The deterministic scheme of Emiris and Canny [1] was the first efficient scheme and is extended in a consistent manner, most notably to the InSphere primitive. We introduce a variant scheme, applicable to a restricted class of algorithms, which is almost optimal in terms of algebraic as well as bit complexity. Neither scheme requires any symbolic computation and both are simple to use as illustrated by our implementation of a convex hull algorithm in arbitrary dimension. Empirical results and a concrete application in robotics are presented.
In this paper, we analyze four parallel sorting algorithms (bitonic, column, radix, and sample sort) with the LogP model. LogP characterizes the performance of modern parallel machines with a small set of parameters: ...
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In this paper, we analyze four parallel sorting algorithms (bitonic, column, radix, and sample sort) with the LogP model. LogP characterizes the performance of modern parallel machines with a small set of parameters: the communication latency (L), overhead (o), bandwidth (g), and the number of processors (P). We develop implementations of these algorithms in Split-C, a parallel extension to C, and compare the performance predicted by LogP to actual performance on a CM-5 of 32 to 512 processors for a range of problem sizes. We evaluate the robustness of the algorithms by varying the distribution and ordering of the key values. We also briefly examine the sensitivity of the algorithms to the communication parameters. We show that the LogP model is a valuable guide in the development of parallel algorithms and a good predictor of implementation performance. The model encourages the use of data layouts which minimize communication and balanced communication schedules which avoid contention. With an empirical model of local processor performance, LogP predictions closely match observed execution times on uniformly distributed keys across a broad range of problem and machine sizes. We find that communication performance is oblivious to the distribution of the key values, whereas the local processor performance is not;some communication phases are sensitive to the ordering of keys due to contention. Finally, our analysis shows that overhead is the most critical communication parameter in the sorting algorithms.
This short note presents the view that microprogramming affords a technology that can provide a powerful, efficient, and versatile computer facility for numerical analysts. Particular areas of application are discusse...
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This short note presents the view that microprogramming affords a technology that can provide a powerful, efficient, and versatile computer facility for numerical analysts. Particular areas of application are discussed. Fundamental questions are raised relevant to the exploitation of this technology by numerical analysts.
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