Computation of matrix chain products on parallel machines

Oded Schwartz; Elad Weiss

doi:10.1109/IPDPS.2019.00059

Computation of matrix chain products on parallel machines

Oded Schwartz, Elad Weiss

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

The Matrix Chain Ordering Problem is a well studied optimization problem, aiming at finding optimal parentheses assignment for minimizing the number of arithmetic operations required when computing a chain of matrix multiplications. Existing algorithms include the O(N³) dynamic programming of Godbole (1973) and the faster O(N log N) algorithm of Hu and Shing (1982). We show that both may result in suboptimal parentheses assignment on modern machines as they do not take into account inter-processor communication costs that often dominate the running time. Further, the optimal solution may change when using fast matrix multiplication algorithms. We show that the O(N³) dynamic-programing algorithm easily adapts to provide optimal solutions for modern matrix multiplication algorithms, and obtain an adaption of the O(N log N) algorithm that guarantees a constant approximation.

Original language	English
Title of host publication	Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	491-500
Number of pages	10
ISBN (Electronic)	9781728112466
DOIs	https://doi.org/10.1109/IPDPS.2019.00059
State	Published - May 2019
Event	33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 - Rio de Janeiro, Brazil Duration: 20 May 2019 → 24 May 2019

Publication series

Name	Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019

Conference

Conference	33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019
Country/Territory	Brazil
City	Rio de Janeiro
Period	20/05/19 → 24/05/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE

Keywords

Algorithms
Fast Matrix Multiplication
I/O Complexity
Matrix Chain Products
Parallel Computation

Access to Document

10.1109/IPDPS.2019.00059

Cite this

Schwartz, O., & Weiss, E. (2019). Computation of matrix chain products on parallel machines. In Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019 (pp. 491-500). Article 8820783 (Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IPDPS.2019.00059

Schwartz, Oded ; Weiss, Elad. / Computation of matrix chain products on parallel machines. Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 491-500 (Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019).

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Schwartz, O & Weiss, E 2019, Computation of matrix chain products on parallel machines. in Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019., 8820783, Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019, Institute of Electrical and Electronics Engineers Inc., pp. 491-500, 33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019, Rio de Janeiro, Brazil, 20/05/19. https://doi.org/10.1109/IPDPS.2019.00059

Computation of matrix chain products on parallel machines. / Schwartz, Oded; Weiss, Elad.
Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 491-500 8820783 (Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Schwartz O, Weiss E. Computation of matrix chain products on parallel machines. In Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 491-500. 8820783. (Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019). doi: 10.1109/IPDPS.2019.00059

Computation of matrix chain products on parallel machines

Abstract

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Bibliographical note

Keywords

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