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Approximations for the general block distribution of a matrix
Responsible organisation
2001 (English)In: Theoretical Computer Science, ISSN 0304-3975, Vol. 262, no 1-2, 145-160 p.Article in journal (Refereed) Published
Abstract [en]

The general block distribution of a matrix is a rectilinear partition of the matrix into orthogonal blocks such that the maximum sum of the elements within a single block is minimized. This corresponds to partitioning the matrix onto parallel processors so as to minimize processor load while maintaining regular communication patterns. Applications of the problem include various parallel sparse matrix computations, compilers for high-performance languages, particle in cell computations, video and image compression, and simulations associated with a communication network. We analyze the performance guarantee of a natural and practical heuristic based on iterative refinement, which has previously been shown to give good empirical results. When p2 is the number of blocks, we show that the tight performance ratio is Theta(rootp). When the matrix has rows of large cost, the details of the objective function of the algorithm are shown to be important, since a naive implementation can lead to a Ohm (p) performance ratio. Extensions to more general cost functions, higher-dimensional arrays, and randomized initial configurations are also considered. (C) 2001 Elsevier Science B.V. All rights reserved.

Place, publisher, year, edition, pages
AMSTERDAM: ELSEVIER SCIENCE BV , 2001. Vol. 262, no 1-2, 145-160 p.
National Category
Software Engineering
Identifiers
URN: urn:nbn:se:bth-8209ISI: 000169594100009Local ID: oai:bth.se:forskinfo15FF76F262DA96A1C12575B00020C316OAI: oai:DiVA.org:bth-8209DiVA: diva2:835898
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2015-06-30Bibliographically approved

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