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      Cartesian partitioning models for 2D and 3D parallel SpGEMM algorithms

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      Author(s)
      Demirci, Gündüz Vehbi
      Aykanat, Cevdet
      Date
      2020
      Source Title
      IEEE Transactions on Parallel and Distributed Systems
      Print ISSN
      1045-9219
      Publisher
      IEEE
      Volume
      31
      Issue
      12
      Pages
      2763 - 2775
      Language
      English
      Type
      Article
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      Abstract
      The focus is distributed-memory parallelization of sparse-general-matrix-multiplication (SpGEMM). Parallel SpGEMM algorithms are classified under one-dimensional (1D), 2D, and 3D categories denoting the number of dimensions by which the 3D sparse workcube representing the iteration space of SpGEMM is partitioned. Recently proposed successful 2D- and 3D-parallel SpGEMM algorithms benefit from upper bounds on communication overheads enforced by 2D and 3D cartesian partitioning of the workcube on 2D and 3D virtual processor grids, respectively. However, these methods are based on random cartesian partitioning and do not utilize sparsity patterns of SpGEMM instances for reducing the communication overheads. We propose hypergraph models for 2D and 3D cartesian partitioning of the workcube for further reducing the communication overheads of these 2D- and 3D- parallel SpGEMM algorithms. The proposed models utilize two- and three-phase partitioning that exploit multi-constraint hypergraph partitioning formulations. Extensive experimentation performed on 20 SpGEMM instances by using upto 900 processors demonstrate that proposed partitioning models significantly improve the scalability of 2D and 3D algorithms. For example, in 2D-parallel SpGEMM algorithm on 900 processors, the proposed partitioning model respectively achieves 85 and 42 percent decrease in total volume and total number of messages, leading to 1.63 times higher speedup compared to random partitioning, on average.
      Keywords
      Sparse matrix-matrix multiplication
      SpGEMM
      Sparse SUMMA SpGEMM
      Split-3D-SpGEMM
      Hypergraph partitioning
      Communication cost
      Bandwidth
      Latency
      Permalink
      http://hdl.handle.net/11693/55081
      Published Version (Please cite this version)
      https://dx.doi.org/10.1109/TPDS.2020.3000708
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