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An optimal parallel algorithm for computing a near-optimal order of matrix multiplications

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Czumaj, Artur (1992) An optimal parallel algorithm for computing a near-optimal order of matrix multiplications. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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Abstract

This paper considers the computation of matrix chain products of the form M1 x M2 x ... M(n-1). The order in which the matrices are multiplied affects the number of operations. The best sequential algorithm for computing an optimal order of matrix multiplication runs in O (n log n) time while the best known parallel NC algorithm runs in O (log2n) time using n6/log6n processors. This paper presents the first approximating optimal parallel algorithm for this problem and for the problem of finding a near-optimal triangulation of a convex polygon. The algorithm runs in O (log n) time using n /logn processors on a CREW PRAM, and O ( log log n) time using n / log log n processors on a weak CRCW PRAM. It produces an order of matrix multiplications and a partition of polygon which differ from the optimal ones at most 0.1547 times.

Item Type: Report
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Matrices, Parallel processing (Electronic computers)
Series Name: Department of Computer Science research report
Publisher: University of Warwick. Department of Computer Science
Official Date: February 1992
Dates:
DateEvent
February 1992Completion
Number: Number 224
Number of Pages: 18
DOI: CS-RR-224
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Reuse Statement (publisher, data, author rights): A.&nbsp;Czumaj, &ldquo;An Optimal Parallel Algorithm for Computing a Near-Optimal Order of Matrix Multiplications&rdquo;, <i>Algorithm Theory</i>, Lecture Notes in Computer Science 621, ed.&nbsp;O.&nbsp;Nurmi and E.&nbsp;Ukkonen, Springer-Verlag, Berlin, pp.&nbsp;62-72 (1992); Proceedings of the 3rd Scandinavian Workshop on Algorithm Theory, Helsinki, July 1992 (SWAT '92)
Grant number: KBN 2-11-90-91-01
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