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VLSI Design
Volume 9 (1999), Issue 1, Pages 69-81
doi:10.1155/1999/32697

Multiplication of Matrices With Different Sparseness Properties on Dynamically Reconfigurable Meshes

Martin Middendorf,1 Hartmut Schmeck,1 Heiko Schröder,2 and Gavin Turner3

1lnstitut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, Karlsruhe D-76128, Germany
2Department of Computer Studies, University of Loughborough, Loughborough LE11 3TU, United Kingdom
3Department of Computer Science, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand

Received 5 May 1997

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Algorithms for multiplying several types of sparse n x n-matrices on dynamically reconfigurable n x n-arrays are presented. For some classes of sparse matrices constant time algorithms are given, e.g., when the first matrix has at most kn elements in each column or in each row and the second matrix has at most kn nonzero elements in each row, where k is a constant. Moreover, O(kn ) algorithms are obtained for the case that one matrix is a general sparse matrix with at most kn nonzero elements and the other matrix has at most k nonzero elements in every row or in every column. Also a lower bound of Ω(Kn ) is proved for this and other cases which shows that the algorithms are close to the optimum.