Accession Number : ADA561679


Title :   Communication Avoiding and Overlapping for Numerical Linear Algebra


Descriptive Note : Technical rept.


Corporate Author : CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE


Personal Author(s) : Georganas, Evangelos ; Gonzalez-Dominguez, Jorge ; Solomonik, Edgar ; Zheng, Yili ; Tourino, Juan ; Yelick, Katherine A


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a561679.pdf


Report Date : 08 May 2012


Pagination or Media Count : 20


Abstract : 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.


Descriptors :   *LINEAR ALGEBRA , ALGORITHMS , COMMUNICATION AND RADIO SYSTEMS , COMPUTER PROGRAMS , CRITICAL PATH METHODS , NUMERICAL ANALYSIS , OVERLAP


Subject Categories : Theoretical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE