Section: New Results

Lower Bounds for the Inherent Data Locality Properties of Computations

Participants : Venmugil Elango [OSU, Columbus, USA] , Louis-Noël Pouchet [UCLA, Los Angeles, USA] , P. Sadayappan [OSU, Columbus, USA] , J. (Ram) Ramanujam [LSU, Houston, USA] , Fabrice Rastello.

Data movement will account for most of the energy as well as execution time on upcoming exascale architectures, including data movement between processors as well as data movement across the memory hierarchy within each processor. Therefore a fundamental characterization of the data access complexity of algorithms is increasingly important.

We addressed the problem of data access or I/O complexity in a two-level memory hierarchy, as studied in the seminal work of Hong and Kung  [26] . We developed a novel approach based on graph min-cut for deriving lower bounds on I/O complexity with two significant advantages over the S-partitioning model of Hong and Kung: (1) the approach can be used to develop analytical expressions with tighter lower bounds for I/O, and (2) unlike any previous model, our new lower bound approach can be automated for analyzing an arbitrary computational directed acyclic graph. We show tighter analytically-derived lower bounds as well as very promising experimental results thanks to a prototype tool that implements our fully-automated analysis.

This work has been submitted and is part of an informal collaboration with P. Sadayappan from the University of Columbus (CSU).