Skip to main content
Springer Nature Link
Log in

SMOaaS: a Scalable Matrix Operation as a Service model in Cloud

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

Matrix operations are fundamental to a wide range of scientific applications such as Graph Theory, Linear Equation System, Image Processing, Geometric Optics, and Probability Analysis. As the workload in these applications has increased, the sizes of matrices involved have also significantly increased. Parallel execution of matrix operations in existing cluster-based systems performs effectively for relatively small matrices but significantly suffers as matrices become larger due to limited resources. Cloud Computing offers scalable resources to handle this limitation; however, the benefits of having access to almost-infinite scalable resources in the Cloud also come with challenges of ensuring time and resource-efficient matrix operations. To the best of our knowledge, there is no specific Cloud service that optimizes the efficiency of matrix operations on Cloud infrastructure. To address this gap and offer convenient service of matrix operations, the paper proposes a novel scalable service framework called Scalable Matrix Operation as a Service. Our framework uses Dynamic Matrix Partition techniques, based on matrix operation and sizes, to achieve efficient work distribution, and scales based on demand to achieve time and resource-efficient operations. The framework also embraces the basic features of security, fault tolerance, and reliability. Experimental results show that the adopted dynamic partitioning technique ensures faster and better performance when compared to the existing static partitioning technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Fiedler M (1975) A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czech Math J 25(4):619–633

    Article  MathSciNet  Google Scholar 

  2. Campbell SL, Meyer CD (2009) Generalized inverses of linear transformations. SIAM, Philadelphia

    Book  Google Scholar 

  3. Mitzenmacher M, Upfal E (2017) Probability and computing: randomization and probabilistic techniques in algorithms and data analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  4. Krishnan M, Nieplocha J (2004) SRUMMA: a matrix multiplication algorithm suitable for clusters and scalable shared memory systems. In: 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings, p 70. IEEE

  5. Dean J, Ghemawat S (2008) Mapreduce: simplified data processing on large clusters. Commun ACM 51(1):107–113

    Article  Google Scholar 

  6. Gittens A, Devarakonda A, Racah E, Ringenburg M, Gerhardt L, Kottalam J, Liu J, Maschhoff K, Canon S, Chhugani J et al (2016) Matrix factorizations at scale: a comparison of scientific data analytics in spark and C+ MPI using three case studies. In: 2016 IEEE International Conference on Big Data (Big Data). IEEE, pp 204–213

  7. Gupta V, Wang S, Courtade T, Ramchandran K (2018) Oversketch: approximate matrix multiplication for the cloud. In: 2018 IEEE International Conference on Big Data (Big Data). IEEE, pp 298–304

  8. Beaumont O, Boudet V, Rastello F, Robert Y et al (2002) Partitioning a square into rectangles: NP-completeness and approximation algorithms. Algorithmica 34(3):217–239

    Article  MathSciNet  Google Scholar 

  9. Pichel JC, Rivera FF (2013) Sparse matrix vector multiplication on the single-chip cloud computer many-core processor. J Parallel Distrib Comput 73(12):1539–1550 (Heterogeneity in Parallel and Distributed Computing)

    Article  Google Scholar 

  10. Yang X, Parthasarathy S, Sadayappan P (2011) Fast sparse matrix-vector multiplication on GPUs: implications for graph mining. Proc VLDB Endow 4(4):231–242

    Article  Google Scholar 

  11. Ashari A, Sedaghati N, Eisenlohr J, Parthasarath S, Sadayappan P (2014) Fast sparse matrix-vector multiplication on GPUs for graph applications. In: SC ’14:Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pp 781–792

  12. Boukaram W, Turkiyyah G, Keyes D (2019) Hierarchical matrix operations on GPUs: matrix-vector multiplication and compression. ACM Trans Math Softw 45(1):1–28

    Article  MathSciNet  Google Scholar 

  13. Seo S, Yoon EJ, Kim J, Jin S, Kim J, Maeng S (2010) Hama: an efficient matrix computation with the mapreduce framework. In: 2010 IEEE Second International Conference on Cloud Computing Technology and Science, pp 721–726

  14. Gu R, Tang Y, Wang Z, Wang S, Yin X, Yuan C, Huang Y (2015) Efficient large scale distributed matrix computation with spark. In: 2015 IEEE International Conference on Big Data (Big Data), pp 2327–2336

  15. Liu J, Liang Y, Ansari N (2016) Spark-based large-scale matrix inversion for big data processing. IEEE Access 4:2166–2176

    Article  Google Scholar 

  16. DeFlumere A, Lastovetsky A (2014) Searching for the optimal data partitioning shape for parallel matrix matrix multiplication on 3 heterogeneous processors. In: 2014 IEEE International Parallel and Distributed Processing Symposium Workshops. IEEE, pp 17–28

  17. Dovolnov E, Kalinov A, Klimov S (2003) Natural block data decomposition for heterogeneous clusters. In: Proceedings International Parallel and Distributed Processing Symposium. IEEE, p 10

  18. Lastovetsky Alexey (2007) On grid-based matrix partitioning for heterogeneous processors. In: Sixth International Symposium on Parallel and Distributed Computing (ISPDC’07). IEEE, p 51

  19. Clarke D, Lastovetsky A, Rychkov V (2012) Column-based matrix partitioning for parallel matrix multiplication on heterogeneous processors based on functional performance models. In: Euro-Par 2011: Parallel Processing Workshops. Springer, Berlin, pp 450–459

  20. Malik T, Rychkov V, Lastovetsky A (2016) Network-aware optimization of communications for parallel matrix multiplication on hierarchical hpc platforms. Concurr Comput Pract Exp 28(3):802–821

    Article  Google Scholar 

  21. Wang S, Huang J, Lee W, Lee K (2018) Scaling up matrix factorization with cloud computing for collaborative recommendation. In: 2018 International Conference on System Science and Engineering (ICSSE), pp 1–6

  22. Gupta V, Wang S, Courtade T, Ramchandran K (2018) Oversketch: approximate matrix multiplication for the cloud. pp 298–304

  23. Qian Z, Chen X, Kang N, Chen M, Yu Y, Moscibroda T, Zhang Z (2012) Madlinq: large-scale distributed matrix computation for the cloud. In: Proceedings of the 7th ACM European Conference on Computer Systems, EuroSys 12, New York, NY, USA. Association for Computing Machinery, p 197210

  24. Beaumont O, Becker BA, DeFlumere A, Eyraud-Dubois L, Lambert T, Lastovetsky A (2019) Recent advances in matrix partitioning for parallel computing on heterogeneous platforms. IEEE Trans Parallel Distrib Syst 30(1):218–229

    Article  Google Scholar 

  25. Chen Y, Xiao G, Fan W, Tang Z, Li K (2020) tpSpMV: a two-phase large-scale sparse matrix-vector multiplication kernel for manycore architectures. Inf Sci 523:279–295

    Article  Google Scholar 

  26. Garg S, Forbes-Smith N, Hilton J, Prakash M (2018) SparkCloud: a cloud-based elastic bushfire simulation service. Remote Sens 10(1):74

    Article  Google Scholar 

  27. Nectar Cloud (2019) https://nectar.org.au/research-cloud/. Accessed 12 May 2018

  28. Jeremy Unruh (2019) Openstack4j. http://www.openstack4j.com/. Accessed 20 Feb 2019

Download references

Author information

Authors and Affiliations

  1. Discipline of ICT, University of Tasmania, Hobart, Australia

    Ujjwal KC, Sudheer Kumar Battula, Saurabh Garg, Ranesh Kumar Naha, Md Anwarul Kaium Patwary & Alexander Brown

Authors
  1. Ujjwal KC
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sudheer Kumar Battula
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saurabh Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ranesh Kumar Naha
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Md Anwarul Kaium Patwary
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Alexander Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ujjwal KC.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ujjwal, K., Battula, S.K., Garg, S. et al. SMOaaS: a Scalable Matrix Operation as a Service model in Cloud. J Supercomput 77, 3381–3401 (2021). https://doi.org/10.1007/s11227-020-03400-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-020-03400-0

Keywords