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International Conference on Parallel Processing and Applied Mathematics

PPAM 2013: Parallel Processing and Applied Mathematics pp 663–672Cite as

An Efficient Representation on GPU for Transition Rate Matrices for Markov Chains

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

The authors present a novel modification of the HYB format — known from the CUSP library. The new format is suitable for sparse Markovian transition rate matrices and enables processing two times bigger matrices on single GPU, also improving computation performance at the same time. Particularly, the SpMV operation — that is the multiplication of a sparse matrix by a vector — is analyzed for this format on one GPU and two GPUs. Numerical experiments for transition rate matrices of Markov chains from [18] show that the proposed format allows to process matrices of sizes about \(3.6 \times 10^7\) rows with the use of single GPU (3 GB RAM). When the plain HYB format is used the matrices of these sizes do not fit in one GPUs memory. Moreover, the use of the modified HYB format can give the speedup even up to 13 times in comparison to multi-threaded CPU (12 cores).

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Acknowledgments

This work was partially supported within the project N N516 479640 of the Ministry of Science and Higher Education (MNiSW) of the Polish Republic “Modele dynamiki transmisji, sterowania zatłoczeniem i jakością usług w Internecie”.

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Authors and Affiliations

  1. Institute of Mathematics, Marie Curie-Skłodowska University, Lublin, Poland

    Jarosław Bylina, Beata Bylina & Marek Karwacki

Authors
  1. Jarosław Bylina
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  2. Beata Bylina
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  3. Marek Karwacki
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Corresponding author

Correspondence to Jarosław Bylina .

Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Bylina, J., Bylina, B., Karwacki, M. (2014). An Efficient Representation on GPU for Transition Rate Matrices for Markov Chains. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_62

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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