Parallel algorithm for the matrix chain product problem
Czumaj, A. (1992) Parallel algorithm for the matrix chain product problem. Technical Report. Department of Computer Science, Coventry, UK.
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This paper considers the problem of finding an optimal order of the multiplication chain of matrices. All parallel algorithms known use the dynamic programming approach and run in a polylogarithmic time using, in the best case, n <sup>6</sup>/log<sup>6</sup>n processors. Our algorithm uses a different approach and reduces the problem to computing some recurrence on a tree. We show that this recurrence can be optimally solved which enables us to improve the parallel bound by a few factors. Our algorithm runs in O (log<sup>3</sup> n) time using n<sup>2</sup>/log<sup>3</sup>n processors on a CREW PRAM and O(log<sup>2</sup> n log log n ) time using n <sup>2</sup>/(log<sup>2</sup>n log log n)processors on a CRCW PRAM. This algorithm solves also the problem of finding an optimal triangulation in a convex polygon. We show that for a monotone polygon this result can be even improved to get an O(log<sup>2</sup>n) time and n processor algorithm on a CREW PRAM.
|Item Type:||Monograph (Technical Report)|
|Uncontrolled Keywords:||technicalreport, parallel algorithms|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty of Science > Computer Science|
|Depositing User:||Mr Ebrahim Ardeshir|
|Date Deposited:||18 Dec 2011 14:38|
|Last Modified:||01 Nov 2012 18:06|
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