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

Faouzi Ben Charrada;  Sana Ezouaoui;  Zaher Mahjoub — 2011

RAIRO - Operations Research - Recherche Opérationnelle

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 ( full) or lower/upper triangular. Given a matrix chain of length , we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O( ) complexity. We then design and analyse two optimal O() greedy algorithms leading in general to different optimal...

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

Faouzi Ben Charrada;  Sana Ezouaoui;  Zaher Mahjoub — 2011

RAIRO - Operations Research

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 ( full) or lower/upper triangular. Given a matrix chain of length , we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O( ) complexity. We then design and analyse two optimal O() greedy algorithms leading in general to different optimal...

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