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International Conference on Parallel Processing and Applied Mathematics

PPAM 2013: Parallel Processing and Applied Mathematics pp 15–25Cite as

Exploiting Data Sparsity in Parallel Matrix Powers Computations

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

Abstract

We derive a new parallel communication-avoiding matrix powers algorithm for matrices of the form \(A=D+USV^H\), where \(D\) is sparse and \(USV^H\) has low rank and is possibly dense. We demonstrate that, with respect to the cost of computing \(k\) sparse matrix-vector multiplications, our algorithm asymptotically reduces the parallel latency by a factor of \(O(k)\) for small additional bandwidth and computation costs. Using problems from real-world applications, our performance model predicts up to \(13\times \) speedups on petascale machines.

Keywords

  • Communication-avoiding
  • Matrix powers
  • Graph cover
  • Hierarchical matrices
  • Parallel algorithms

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Authors and Affiliations

  1. University of California, Berkeley, USA

    Nicholas Knight, Erin Carson & James Demmel

Authors
  1. Nicholas Knight
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  2. Erin Carson
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  3. James Demmel
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Corresponding author

Correspondence to Nicholas Knight .

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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Knight, N., Carson, E., Demmel, J. (2014). Exploiting Data Sparsity in Parallel Matrix Powers Computations. 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_2

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

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