Volume 45, Number 1, January-March 2011
|Page(s)||1 - 16|
|Published online||14 March 2011|
Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices
University of Tunis El Manar, Faculty of Sciences of Tunis, Campus Universitaire 2092
Manar II, Tunis, Tunisia; email@example.com; firstname.lastname@example.org; email@example.com
Accepted: 14 December 2010
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.
Mathematics Subject Classification: 65K05 / 90C27 / 90C39 / 90C59
Key words: Combinatorial optimization / dynamic programming / gree-dy algorithm / matrix chain product / parallel computing
© EDP Sciences, ROADEF, SMAI, 2011
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