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Greedy algorithms for optimal computing of matrix chain products involving square denseand triangular matrices

Published online by Cambridge University Press:  14 March 2011

Faouzi Ben Charrada ,
Sana Ezouaoui  and
Zaher Mahjoub
Faouzi Ben Charrada
Affiliation:
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universitaire 2092 Manar II, Tunis, Tunisia; f.charrada@gnet.tn; zwawi_sana@yahoo.fr; zaher.mahjoub@fst.rnu.tn
Sana Ezouaoui
Affiliation:
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universitaire 2092 Manar II, Tunis, Tunisia; f.charrada@gnet.tn; zwawi_sana@yahoo.fr; zaher.mahjoub@fst.rnu.tn
Zaher Mahjoub
Affiliation:
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universitaire 2092 Manar II, Tunis, Tunisia; f.charrada@gnet.tn; zwawi_sana@yahoo.fr; zaher.mahjoub@fst.rnu.tn
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Abstract

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions i.e. chain parenthesizations. Afterwards, we establish a comparison between these two algorithms based on the parallel computing of the matrix chain product through intra and inter-subchains coarse grain parallelism. Finally, an experimental study illustrates the theoretical parallel performances of the designed algorithms.

Keywords

Combinatorial optimizationdynamic programminggree-dy algorithmmatrix chain productparallel computing
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 1 , January 2011 , pp. 1 - 16
Copyright
© EDP Sciences, ROADEF, SMAI, 2011

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