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Publications of SPCL
|G. Kwasniewski, M. Kabić, M. Besta, J. VandeVondele, R. Solcà, T. Hoefler:|
|Red-Blue Pebbling Revisited: Near Optimal Parallel Matrix-Matrix Multiplication|
(In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC19), Nov. 2019, )
Best Paper Finalist, SC19 Best Student Paper (1/87)
AbstractWe propose COSMA: a parallel matrix-matrix multiplication algorithm that is near communication-optimal for all combinations of matrix dimensions, processor counts, and memory sizes. The key idea behind COSMA is to derive an optimal (up to a factor of 0.03% for 10MB of fast memory) sequential schedule and then parallelize it, preserving I/O optimality. To achieve this, we use the red-blue pebble game to precisely model MMM dependencies and derive a constructive and tight sequential and parallel I/O lower bound proofs. Compared to 2D or 3D algorithms, which fix processor decomposition upfront and then map it to the matrix dimensions, it reduces communication volume by up to 3 times. COSMA outperforms the established ScaLAPACK, CARMA, and CTF algorithms in all scenarios up to 12.8x (2.2x on average), achieving up to 88% of Piz Daint’s peak performance. Our work does not require any hand tuning and is maintained as an open source implementation.
access preprint on arxiv:
Recorded talk (best effort)