This work studies the application of the discrete Hölder-Brascamp-Lieb (HBL) inequalities to the design of communication optimal algorithms. In particular, it describes optimal tiling (blocking) strategies for nested loops that lack data dependencies and exhibit linear memory access patterns. We attain known lower bounds for communication costs by unraveling the relationship between the HBL linear program, its dual, and tile selection. The methods used are constructive and algorithmic. The case when all arrays have one index is explored in depth, as a useful example in which a particularly efficient tiling can be determined.
Title
Parallelepipeds obtaining HBL lower bounds
Published
2016-11-13
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2016-162
Type
Text
Extent
25 p
Archive
The Engineering Library
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