Parallelepipeds obtaining HBL lower bounds

James Demmel and Alex Rusciano

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2016-162
November 13, 2016

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-162.pdf

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.


BibTeX citation:

@techreport{Demmel:EECS-2016-162,
    Author = {Demmel, James and Rusciano, Alex},
    Title = {Parallelepipeds obtaining HBL lower bounds},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2016},
    Month = {Nov},
    URL = {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-162.html},
    Number = {UCB/EECS-2016-162},
    Abstract = {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.}
}

EndNote citation:

%0 Report
%A Demmel, James
%A Rusciano, Alex
%T Parallelepipeds obtaining HBL lower bounds
%I EECS Department, University of California, Berkeley
%D 2016
%8 November 13
%@ UCB/EECS-2016-162
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-162.html
%F Demmel:EECS-2016-162