research-article

In-memory data compression for sparse matrices

Author:

Orion Sky LawlorAuthors Info & Claims

IA³ '13: Proceedings of the 3rd Workshop on Irregular Applications: Architectures and Algorithms

Article No.: 6, Pages 1 - 6

https://doi.org/10.1145/2535753.2535758

Published: 17 November 2013 Publication History

Get Access

Abstract

We present a high performance in-memory lossless data compression scheme designed to save both memory storage and bandwidth for general sparse matrices. Because the storage hierarchy is increasingly becoming the limiting factor in overall delivered machine performance, this type of data structure compression will become increasingly important. Compared to conventional compressed sparse row (CSR) using 32-bit column indices, compressed column indices (CCI) can be over 90% smaller, yet still be decompressed at tens of gigabytes per second. We present time and space savings for 20 standard sparse matrices, on multicore CPUs and modern GPUs.

References

[1]

N. Bell and M. Garland. Efficient sparse matrix-vector multiplication on CUDA. NVIDIA Technical Report NVR-2008-004, 2008.

Google Scholar

[2]

P. N. Brown and A. C. Hindmarsh. Matrix-free methods for stiff systems of ODEs. SIAM J. Numer. Anal., 23(3): 610--638, 1986.

Digital Library

Google Scholar

[3]

Y. Collet. LZ4: Extremely fast compression algorithm. In code.google.com, 2013.

Google Scholar

[4]

T. A. Davis and Y. Hu. The university of Florida sparse matrix collection. ACM Transactions on Mathematical Software, 38: 1--25, 2011.

Digital Library

Google Scholar

[5]

O. Edfors, P. O. Börjesson, A. Erendi, P. Ola, and B. S. A. Erendi. Analysis of a fast algorithm for look-up table based variable-length decoding. In Proc. Radioveten. Konf, pages 181--184, 1993.

Google Scholar

[6]

D. A. Huffman. A method for the construction of minimum redundancy codes. Proceedings of the I.R.E., 40: 1098--1101, 1951.

Crossref

Google Scholar

[7]

S. W. Keckler, W. J. Dally, B. K. Khailany, M. Garland, and D. Glasco. GPUs and the future of parallel computing. IEEE Micro, 31(5): 7--17, 2011.

Digital Library

Google Scholar

[8]

O. S. Lawlor, S. Chakravorty, T. L. Wilmarth, N. Choudhury, I. Dooley, G. Zheng, and L. V. Kale. ParFUM: A parallel framework for unstructured meshes for scalable dynamic physics applications. Engineering With Computers, 22(3): 215--235, 2006.

Digital Library

Google Scholar

[9]

N. Reddy, R. Prakash, and R. M. Reddy. New sparse matrix storage format to improve the performance of total SPMV time. Scalable Computing: Practice and Experience, 13(2): 159--171, 2012.

Google Scholar

[10]

M. Schindler. Practical Huffman coding. http://www.compressconsult.com/huffman/, August 1998.

Google Scholar

[11]

C. Shannon. A mathematical theory of communication. Bell System Technical Journal, pages 379--423, July 1948.

Google Scholar

[12]

T. Summers. Hardware based GZIP compression, benefits and applications. In AHA Products Group Whitepaper, 2008.

Google Scholar

[13]

R. Telichevesky, K. S. Kundert, and J. K. White. Efficient steady-state analysis based on matrix-free krylov-subspace methods. In Proceedings of the 32nd annual ACM/IEEE Design Automation Conference, pages 480--484. ACM, 1995.

Digital Library

Google Scholar

[14]

J. Willcock and A. Lumsdaine. Accelerating sparse matrix computations via data compression. In Proceedings of the 20th annual international conference on Supercomputing, ICS '06, pages 307--316, New York, NY, USA, 2006. ACM.

Digital Library

Google Scholar

Cited By

View all

Wu GZhou FDing GWu QLi X(2023)An Efficient Heterogeneous Edge-Cloud Learning Framework for Spectrum Data CompressionIEEE Transactions on Mobile Computing10.1109/TMC.2022.315304922:7(3823-3839)Online publication date: 1-Jul-2023
https://doi.org/10.1109/TMC.2022.3153049
Lindquist NLuszczek PDongarra J(2022)Accelerating Restarted GMRES With Mixed Precision ArithmeticIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2021.309075733:4(1027-1037)Online publication date: 1-Apr-2022
https://doi.org/10.1109/TPDS.2021.3090757
Kulasiri DKosarwal RKulasiri DKosarwal R(2021)Visualizing Markov Process Through Graphs and TreesChemical Master Equation for Large Biological Networks10.1007/978-981-16-5351-3_3(55-80)Online publication date: 12-Sep-2021
https://doi.org/10.1007/978-981-16-5351-3_3
Show More Cited By

Recommendations

Distributed-memory hierarchical compression of dense SPD matrices
SC '18: Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis

We present a distributed memory algorithm for the hierarchical compression of symmetric positive definite (SPD) matrices. Our method is based on GOFMM, an algorithm that appeared in doi:10.1145/3126908.3126921. For many SPD matrices, GOFMM enables ...
External memory algorithms for factoring sparse matrices
Crout Versions of ILU for General Sparse Matrices
^* Copper Mountain Special Issue on Iterative Methods

This paper presents an efficient implementation of the incomplete LU (ILU) factorization derived from the Crout version of Gaussian elimination. At step k of the elimination, the kth row of U and the kth column of L are computed using previously computed ...

Comments

Information & Contributors

Information

Published In

IA³ '13: Proceedings of the 3rd Workshop on Irregular Applications: Architectures and Algorithms

November 2013

92 pages

ISBN:9781450325035

DOI:10.1145/2535753

Conference Chairs:
Antonino Tumeo
PNNL
,
John Feo
PNNL
,
Oreste Villa
NVIDIA
,
Simone Secchi
Università di Cagliari, Italy

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 November 2013

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Research-article

Conference

SC13

Sponsor:

SC13: International Conference for High Performance Computing, Networking, Storage and Analysis

November 17 - 22, 2013

Colorado, Denver

Acceptance Rates

IA³ '13 Paper Acceptance Rate 6 of 21 submissions, 29%;

Overall Acceptance Rate 18 of 67 submissions, 27%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
162
Total Downloads

Downloads (Last 12 months)9
Downloads (Last 6 weeks)1

Reflects downloads up to 12 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Wu GZhou FDing GWu QLi X(2023)An Efficient Heterogeneous Edge-Cloud Learning Framework for Spectrum Data CompressionIEEE Transactions on Mobile Computing10.1109/TMC.2022.315304922:7(3823-3839)Online publication date: 1-Jul-2023
https://doi.org/10.1109/TMC.2022.3153049
Lindquist NLuszczek PDongarra J(2022)Accelerating Restarted GMRES With Mixed Precision ArithmeticIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2021.309075733:4(1027-1037)Online publication date: 1-Apr-2022
https://doi.org/10.1109/TPDS.2021.3090757
Kulasiri DKosarwal RKulasiri DKosarwal R(2021)Visualizing Markov Process Through Graphs and TreesChemical Master Equation for Large Biological Networks10.1007/978-981-16-5351-3_3(55-80)Online publication date: 12-Sep-2021
https://doi.org/10.1007/978-981-16-5351-3_3
Kosarwal RKulasiri DSamarasinghe S(2020)Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networksBMC Bioinformatics10.1186/s12859-020-03668-221:1Online publication date: 11-Nov-2020
https://doi.org/10.1186/s12859-020-03668-2
Rawal AFang YChien A(2019)Programmable Acceleration for Sparse Matrices in a Data-Movement Limited World2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)10.1109/IPDPSW.2019.00016(47-56)Online publication date: May-2019
https://doi.org/10.1109/IPDPSW.2019.00016
Kotthaus HKorb IEngel MMarwedel P(2014)Dynamic page sharing optimization for the R languageACM SIGPLAN Notices10.1145/2775052.266109450:2(79-90)Online publication date: 14-Oct-2014
https://dl.acm.org/doi/10.1145/2775052.2661094
Kotthaus HKorb IEngel MMarwedel PBlack ATratt L(2014)Dynamic page sharing optimization for the R languageProceedings of the 10th ACM Symposium on Dynamic languages10.1145/2661088.2661094(79-90)Online publication date: 20-Oct-2014
https://dl.acm.org/doi/10.1145/2661088.2661094

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Recommendations

Distributed-memory hierarchical compression of dense SPD matrices

External memory algorithms for factoring sparse matrices

Crout Versions of ILU for General Sparse Matrices

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

Login options

Full Access

PDF

eReader

Abstract

References

Cited By

Recommendations

Distributed-memory hierarchical compression of dense SPD matrices

External memory algorithms for factoring sparse matrices

Crout Versions of ILU for General Sparse Matrices

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

Get Access

Login options

Full Access

View options

PDF

eReader

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations