On the Optimal Recovery Threshold of Coded Matrix Multiplication

We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i.e., the required number of successful workers. When a fixed <inline-formula> <tex-math notation="LaTeX"...

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Veröffentlicht in:IEEE transactions on information theory Jg. 66; H. 1; S. 278 - 301
Hauptverfasser: Dutta, Sanghamitra, Fahim, Mohammad, Haddadpour, Farzin, Jeong, Haewon, Cadambe, Viveck, Grover, Pulkit
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Coded computing
Codes
Coding
Computation
Computational complexity
Computational efficiency
Computational modeling
distributed computing
Encoding
Fault tolerance
matrix multiplication
Multiplication
Polynomials
Recovery
recovery threshold
stragglers
Systematics
Workers
ISSN:0018-9448, 1557-9654
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Zusammenfassung:We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i.e., the required number of successful workers. When a fixed <inline-formula> <tex-math notation="LaTeX">1/m </tex-math></inline-formula> fraction of each matrix can be stored at each worker node, Polynomial codes require <inline-formula> <tex-math notation="LaTeX">m^{2} </tex-math></inline-formula> successful workers, while our MatDot codes only require <inline-formula> <tex-math notation="LaTeX">2m-1 </tex-math></inline-formula> successful workers. However, MatDot codes have higher computation cost per worker and higher communication cost from each worker to the fusion node. We also provide a systematic construction of MatDot codes. Furthermore, we propose "PolyDot" coding that interpolates between Polynomial codes and MatDot codes to trade off computation/communication costs and recovery thresholds. Finally, we demonstrate a novel coding technique for multiplying <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> matrices (<inline-formula> <tex-math notation="LaTeX">n \geq 3 </tex-math></inline-formula>) using ideas from MatDot and PolyDot codes.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2929328