Section: New Results

Characterizing the Inherent Data Movement Complexity of Computations via Lower Bounds

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

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a fundamental characterization of data access complexity will be increasingly important. Although the problem of characterizing data access complexity has been modeled previously using the formalism of Hong & Kung's red/blue pebble game  [27] , applicability of previously-developed approaches has been extremely limited. We improve on prior work in several ways: 1) we develop an approach to composing lower bounds from arbitrary decompositions of computational directed acyclic graphs, thereby eliminating a significant limitation of previous approaches that required homogeneity of analyzed computations, 2) we develop a complementary graph min-cut based strategy to Hong & Kung's S-partitioning approach, and 3) we develop an automated approach to generate concrete I/O lower bounds of arbitrary, possibly irregular computational directed acyclic graphs. We provide experimental results demonstrating the utility of the developed approach.

This work has been submitted to PLDI'14 and is part of an informal collaboration with P. Sadayappan from the University of Columbus (OSU) (see Section  8.4 ).