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DTSTAMP:20211207T054809Z
LOCATION:220-221
DTSTART;TZID=America/Chicago:20211118T103000
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UID:submissions.supercomputing.org_SC21_sess161_pap252@linklings.com
SUMMARY:On the Parallel I/O Optimality of Linear Algebra Kernels:  Near-Op
 timal Matrix Factorizations
DESCRIPTION:Paper\n\nOn the Parallel I/O Optimality of Linear Algebra Kern
 els:  Near-Optimal Matrix Factorizations\n\nKwasniewski, Kabić, Ben-N
 un, Ziogas, Saethre...\n\nMatrix factorizations are among the most importa
 nt building blocks of scientific computing. State-of-the-art libraries, ho
 wever, are not communication-optimal, underutilizing current parallel arch
 itectures. We present novel algorithms for Cholesky and LU factorizations 
 that utilize an asymptotically communication-optimal 2.5D decomposition. W
 e first establish a theoretical framework for deriving parallel I/O lower 
 bounds for linear algebra kernels, and then utilize its insights to derive
  Cholesky and LU schedules, both communicating N^3/(P*sqrt(M)) elements pe
 r processor, where M is the local memory size. The empirical results match
  our theoretical analysis: our implementations communicate significantly l
 ess than Intel MKL, SLATE and the asymptotically communication-optimal CAN
 DMC and CAPITAL libraries. Our code outperforms these state-of-the-art lib
 raries in almost all tested scenarios, with matrix sizes ranging from 2048
  to 262,144 on up to 512 CPU nodes of the Piz Daint supercomputer, decreas
 ing the time-to-solution by up to three times. Our code is ScaLAPACK-compa
 tible and available as an open-source library.\n\nTag: Reproducibility Bad
 ge, Algorithms, Architectures, Numerical Algorithms\n\nRegistration Catego
 ry: Tech Program Reg Pass\n\nReproducibility Badges: Artifact Available, A
 rtifact Functional, Results Reproduced
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