SCHEDULE: NOV 10-16, 2012
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Communication Avoiding and Overlapping for Numerical Linear Algebra
SESSION: Linear Algebra Algorithms
EVENT TYPE: Papers
TIME: 3:30PM - 4:00PM
SESSION CHAIR: X. Sherry Li
AUTHOR(S):Evangelos Georganas, Jorge González-Domínguez, Edgar Solomonik, Yili Zheng, Juan Touriño, Katherine Yelick
To efficiently scale dense linear algebra problems to future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve scalability by reducing inter-processor data transfer volume at the cost of extra memory usage. Communication overlap attempts to hide messaging latency by pipelining messages and overlapping with computational work. We study the interaction and compatibility of these two techniques for two matrix multiplication algorithms (Cannon and SUMMA), triangular solve, and Cholesky factorization. For each algorithm, we construct a detailed performance model which considers both critical path dependencies and idle time. We give novel implementations of 2.5D algorithms with overlap for each of these problems. Our software employs UPC, a partitioned global address space (PGAS) language that provides fast one-sided communication. We show communication avoidance and overlap provide a cumulative benefit as core counts scale, including results using over 24K cores of a Cray XE6 system.
X. Sherry Li (Chair) - Lawrence Berkeley National Laboratory
Evangelos Georganas - University of California, Berkeley
Jorge González-Domínguez - University of A Coruna
Edgar Solomonik - University of California, Berkeley
Yili Zheng - Lawrence Berkeley National Laboratory
Juan Touriño - University of A Coruna
Katherine Yelick - Lawrence Berkeley National Laboratory