Red-Blue Pebbling Revisited: Near Optimal Parallel Matrix Multiplication
Event Type
Registration Categories
Linear Algebra
Parallel Programming Languages, Libraries, and Models
Task-based programming
Award Finalists
BP Finalist
BSP Finalist
TimeTuesday, 19 November 20193:30pm - 4pm
DescriptionWe 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 sqrt{3}. 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.
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