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On the parallel I/O optimality of linear algebra kernels: Near-optimal LU factorization
- Conference Paper
© 2021 Owner/Author. Dense linear algebra kernels are fundamental components of many scientific computing applications. In this work we present a novel method of deriving parallel I/O lower bounds for this broad family of programs. Based on the X-Partitioning abstraction, our method explicitly captures inter-statement dependencies. Applying our analysis to LU factorization, we derive COnfLUX, an LU algorithm with the parallel I/O cost of N3/([EQUATION]) communicated elements per processor - only 1/3× over our established lower bound. We evaluate COnfLUX on various problem sizes, demonstrating empirical results that match our theoretical analysis, communicating less than Cray ScaLAPACK, SLATE, and the asymptotically-optimal CANDMC library. Running on 1,024 nodes of Piz Daint, COnfLUX communicates 1.6× less than the second-best implementation and is expected to communicate 2.1× less on a full-scale run on Summit. Show more
Journal / seriesProceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP
Pages / Article No.
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