A new block algorithm for triangularization of regular or singular matrices with dimension m × n is proposed. Taking benefit of fast block multiplication algorithms, it achieves the best known sequential complexi...
ISBN:
(纸本)9781581134094
A new block algorithm for triangularization of regular or singular matrices with dimension m × n is proposed. Taking benefit of fast block multiplication algorithms, it achieves the best known sequential complexity Ο(mw-1n) for any sizes and any rank. Moreover, the block strategy enables to improve locality with respect to previous algorithms as exhibited by practical performances.
Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages...
ISBN:
(纸本)9781581131857
Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. We propose a model for optimizing the exchange of messages under such circumstances which we call the minimum phase remapping problem. We first show that the problem is NP-Complete, and then analyze several methodologies for addressing it. First, we show how the problem can be phrased as an instance of multi-commodity flow. Next, we study a continuous approximation to the problem. We show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. Finally, we devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases.
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