On the optimal recovery threshold of coded matrix multiplication

Mohammad Fahim, Haewon Jeong, Farzin Haddadpour, Sanghamitra Dutta, Viveck Ramesh Cadambe, Pulkit Grover

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

Abstract

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 m-Th fraction of each matrix can be stored in each worker node, polynomial codes require m2 successful workers, while our novel MatDot codes only require 2m-1 successful workers, albeit at a higher communication cost from each worker to the fusion node. Further, we propose 'PolyDot' coding that interpolates between Polynomial codes and MatDot codes. Finally, we demonstrate an application of PolyDot codes to multiplying multiple (> 2) matrices.

Original languageEnglish (US)
Title of host publication55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1264-1270
Number of pages7
ISBN (Electronic)9781538632666
DOIs
StatePublished - Jan 17 2018
Event55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 - Monticello, United States
Duration: Oct 3 2017Oct 6 2017

Publication series

Name55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
Volume2018-January

Other

Other55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
CountryUnited States
CityMonticello
Period10/3/1710/6/17

Fingerprint

Optimal Recovery
Matrix multiplication
Recovery
Polynomials
Polynomial
Fusion reactions
Matrix Product
Communication Cost
Vertex of a graph
Communication
Fusion
Coding
Interpolate
Costs
Demonstrate

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Energy Engineering and Power Technology
  • Control and Optimization

Cite this

Fahim, M., Jeong, H., Haddadpour, F., Dutta, S., Cadambe, V. R., & Grover, P. (2018). On the optimal recovery threshold of coded matrix multiplication. In 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 (pp. 1264-1270). (55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2017.8262882
Fahim, Mohammad ; Jeong, Haewon ; Haddadpour, Farzin ; Dutta, Sanghamitra ; Cadambe, Viveck Ramesh ; Grover, Pulkit. / On the optimal recovery threshold of coded matrix multiplication. 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1264-1270 (55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017).
@inproceedings{9b15024d1c8b466fb817e9bb1a01a481,
title = "On the optimal recovery threshold of coded matrix multiplication",
abstract = "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 m-Th fraction of each matrix can be stored in each worker node, polynomial codes require m2 successful workers, while our novel MatDot codes only require 2m-1 successful workers, albeit at a higher communication cost from each worker to the fusion node. Further, we propose 'PolyDot' coding that interpolates between Polynomial codes and MatDot codes. Finally, we demonstrate an application of PolyDot codes to multiplying multiple (> 2) matrices.",
author = "Mohammad Fahim and Haewon Jeong and Farzin Haddadpour and Sanghamitra Dutta and Cadambe, {Viveck Ramesh} and Pulkit Grover",
year = "2018",
month = "1",
day = "17",
doi = "10.1109/ALLERTON.2017.8262882",
language = "English (US)",
series = "55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1264--1270",
booktitle = "55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017",
address = "United States",

}

Fahim, M, Jeong, H, Haddadpour, F, Dutta, S, Cadambe, VR & Grover, P 2018, On the optimal recovery threshold of coded matrix multiplication. in 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017. 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 1264-1270, 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017, Monticello, United States, 10/3/17. https://doi.org/10.1109/ALLERTON.2017.8262882

On the optimal recovery threshold of coded matrix multiplication. / Fahim, Mohammad; Jeong, Haewon; Haddadpour, Farzin; Dutta, Sanghamitra; Cadambe, Viveck Ramesh; Grover, Pulkit.

55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1264-1270 (55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - On the optimal recovery threshold of coded matrix multiplication

AU - Fahim, Mohammad

AU - Jeong, Haewon

AU - Haddadpour, Farzin

AU - Dutta, Sanghamitra

AU - Cadambe, Viveck Ramesh

AU - Grover, Pulkit

PY - 2018/1/17

Y1 - 2018/1/17

N2 - 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 m-Th fraction of each matrix can be stored in each worker node, polynomial codes require m2 successful workers, while our novel MatDot codes only require 2m-1 successful workers, albeit at a higher communication cost from each worker to the fusion node. Further, we propose 'PolyDot' coding that interpolates between Polynomial codes and MatDot codes. Finally, we demonstrate an application of PolyDot codes to multiplying multiple (> 2) matrices.

AB - 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 m-Th fraction of each matrix can be stored in each worker node, polynomial codes require m2 successful workers, while our novel MatDot codes only require 2m-1 successful workers, albeit at a higher communication cost from each worker to the fusion node. Further, we propose 'PolyDot' coding that interpolates between Polynomial codes and MatDot codes. Finally, we demonstrate an application of PolyDot codes to multiplying multiple (> 2) matrices.

UR - http://www.scopus.com/inward/record.url?scp=85047977021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047977021&partnerID=8YFLogxK

U2 - 10.1109/ALLERTON.2017.8262882

DO - 10.1109/ALLERTON.2017.8262882

M3 - Conference contribution

AN - SCOPUS:85047977021

T3 - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017

SP - 1264

EP - 1270

BT - 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Fahim M, Jeong H, Haddadpour F, Dutta S, Cadambe VR, Grover P. On the optimal recovery threshold of coded matrix multiplication. In 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1264-1270. (55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017). https://doi.org/10.1109/ALLERTON.2017.8262882