Revisiting the I/O-Complexity of Fast Matrix Multiplication with Recomputations

Communication costs, between processors and across the memory hierarchy, often dominate the runtime of algorithms. Can we trade these costs for recomputations? Most algorithms do not utilize recomputation for this end, and most communication cost lower bounds assume no recomputation, hence do not ad...

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Bibliographic Details
Published inProceedings - IEEE International Parallel and Distributed Processing Symposium pp. 482 - 490
Main Authors Nissim, Roy, Schwartz, Oded
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2019
Subjects
Bipartite graph
Complexity theory
Computational modeling
Decoding
Encoding
Fast Fourier transforms
Fast Matrix Multiplication
I/O-complexity
Memory Hierarchy
Parallel Computation
Program processors
Recomputation
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ISSN1530-2075
DOI10.1109/IPDPS.2019.00058

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Summary:Communication costs, between processors and across the memory hierarchy, often dominate the runtime of algorithms. Can we trade these costs for recomputations? Most algorithms do not utilize recomputation for this end, and most communication cost lower bounds assume no recomputation, hence do not address this fundamental question. Recently, Bilardi and De Stefani (2017), and Bilardi, Scquizzato, and Silvestri (2018) showed that recomputations cannot reduce communication costs in Strassen's fast matrix multiplication and in fast Fourier transform. We extend the former bound and show that recomputations cannot reduce communication costs for a few other fast matrix multiplication algorithms.
ISSN:1530-2075
DOI:10.1109/IPDPS.2019.00058