Distributed SBP Cholesky Factorization Algorithms with Near-Optimal Scheduling

Copyright © (2009) by Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distrubuted for profit or commericial advantage. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.

The minimal block storage Distributed Square Block Packed (DSBP) format for distributed memory computing on symmetric and triangular matrices is presented. Three algorithm variants (Basic, Static, and Dynamic) of the blocked right-looking Cholesky factorization are designed for the DSBP format, implemented, and evaluated. On our target machine, all variants outperform standard full storage implementations while saving half the storage. Communication overhead is shown to be virtually eliminated by our Static and Dynamic variants which take advantage of hardware parallelism. The Static and Dynamic variants give nearly the same performance while clearly outperforming the Basic variant which in turn is comparable with standard implementations such as the one found in ScaLAPACK. Models of execution assuming zero communication costs are developed. The Static schedule is near-optimal on our target machine for medium to large problems based on comparisons with these models.

By: Fred Gustavson; Lars Karlsson; Bo Kågström

Published in: ACM Transactions on Mathematical Software , volume 36, (no 2), pages Art. no. 11 in 2009


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