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Downsampling Algorithms for Large Sparse Matrices

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Abstract

Mapping of sparse matrices to processors of a parallel system may have a significant impact on the development of sparse-matrix algorithms and, in effect, to their efficiency. We present and empirically compare two downsampling algorithms for sparse matrices. The first algorithm is independent of particular matrix-processors mapping, while the second one is adapted for cases where matrices are partitioned among processors according to contiguous chunks of rows/columns. We show that the price for the versatility of the first algorithm is the collective communication performed by all processors. The second algorithm uses more efficient communication strategy, which stems from the knowledge of mapping of matrices to processors, and effectively outperforms the first algorithm in terms of running time.

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Acknowledgments

This work was supported by the Czech Science Foundation under Grant No. P202/12/2011. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (award number OCI 07-25070) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana–Champaign and its National Center for Supercomputing Applications. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This work was supported by the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme, as well as Czech Ministry of Education, Youth and Sports via the project Large Research, Development and Innovations Infrastructures (LM2011033). The authors acknowledge helpful advice from J. Šístek.

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Authors and Affiliations

  1. Department of Computer Systems, Faculty of Information Technology, Czech Technical University in Prague, Thákurova 9, 160 00 , Prague, Czech Republic

    Daniel Langr, Pavel Tvrdík & Ivan Šimeček

  2. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803, USA

    Tomáš Dytrych

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  1. Daniel Langr
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  2. Pavel Tvrdík
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  4. Tomáš Dytrych
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Correspondence to Daniel Langr.

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Langr, D., Tvrdík, P., Šimeček, I. et al. Downsampling Algorithms for Large Sparse Matrices. Int J Parallel Prog 43, 679–702 (2015). https://doi.org/10.1007/s10766-014-0315-8

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