Computation of matrix chain products on parallel machines

Oded Schwartz, Elad Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 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 languageAmerican English
Title of host publicationProceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages491-500
Number of pages10
ISBN (Electronic)9781728112466
DOIs
StatePublished - May 2019
Event33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 - Rio de Janeiro, Brazil
Duration: 20 May 201924 May 2019

Publication series

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

Conference

Conference33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019
Country/TerritoryBrazil
CityRio de Janeiro
Period20/05/1924/05/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE

Keywords

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

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