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    Leveraging PaRSEC runtime support to tackle challenging 3D data-sparse matrix problems

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    ipdps2021-initial-submission.pdf
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    Type
    Conference Paper
    Authors
    Cao, Qinglei
    Pei, Yu
    Akbudak, Kadir
    Bosilca, George
    Ltaief, Hatem cc
    Keyes, David E. cc
    Dongarra, Jack
    KAUST Department
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Office of the President
    Date
    2021-05
    Permanent link to this record
    http://hdl.handle.net/10754/665738
    
    Metadata
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    Abstract
    The task-based programming model associated with dynamic runtime systems has gained popularity for challenging problems because of workload imbalance, heterogeneous resources, or extreme concurrency. During the last decade, low-rank matrix approximations - where the main idea consists of exploiting data sparsity, typically by compressing off-diagonal tiles up to an application-specific accuracy threshold - have been adopted to address the curse of dimensionality at extreme scale. In this paper, we create a bridge between the runtime and the linear algebra by communicating knowledge of the data sparsity to the runtime. We design and implement this synergistic approach with high user productivity in mind, in the context of the PaRSEC runtime system and the HiCMA numerical library. This requires extending PaRSEC with new features to integrate rank information into the dataflow so that proper decisions can be made at runtime. We focus on the tile low-rank (TLR) Cholesky factorization for solving 3D data-sparse covariance matrix problems arising in environmental applications. In particular, we employ the 3D exponential model of the Mateŕn matrix kernel, which exhibits challenging nonuniform high ranks in off-diagonal tiles. We first provide dynamic data structure management driven by a performance model to reduce extra floating-point operations. Next, we optimize the memory footprint of the application by relying on a dynamic memory allocator, and supported by a rank-aware data distribution to cope with the workload imbalance. Finally, we expose further parallelism using kernel recursive formulations to shorten the critical path. Our resulting high-performance implementation outperforms existing data-sparse TLR Cholesky factorization by up to 7-fold on a large-scale distributed-memory system, while minimizing the memory footprint up to a 44-fold factor. This multidisciplinary work highlights the need to empower runtime systems beyond their original duty of task scheduling for servicing next-generation low-rank matrix algebra libraries.
    Citation
    Cao, Q., Pei, Y., Akbudak, K., Bosilca, G., Ltaief, H., Keyes, D., & Dongarra, J. (2021). Leveraging PaRSEC Runtime Support to Tackle Challenging 3D Data-Sparse Matrix Problems. 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS). doi:10.1109/ipdps49936.2021.00017
    Sponsors
    This research was partially supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.
    Publisher
    IEEE
    Conference/Event name
    35th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2021
    ISBN
    9781665440660
    DOI
    10.1109/IPDPS49936.2021.00017
    Additional Links
    https://ieeexplore.ieee.org/document/9460493/
    https://repository.kaust.edu.sa/bitstream/10754/665738/1/ipdps2021-initial-submission.pdf
    ae974a485f413a2113503eed53cd6c53
    10.1109/IPDPS49936.2021.00017
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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