Sequential optimization of matrix chain multiplication relative to different cost functions

Authors:
Igor Chikalov;Shahid Hussain;Mikhail Moshkov
Affiliations:
Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;Mathematical and Computer Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Venue:
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Year:
2011

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Abstract

In this paper, we present a methodology to optimize matrix chain multiplication sequentially relative to different cost functions such as total number of scalar multiplications, communication overhead in a multiprocessor environment, etc. For n matrices our optimization procedure requires O(n3) arithmetic operations per one cost function. This work is done in the framework of a dynamic programming extension that allows sequential optimization relative to different criteria.