On Characterizing the Data Access Complexity of Programs

TL;DR

This paper introduces a new static analysis method to derive asymptotic data-access lower bounds for programs, addressing limitations of previous approaches by using graph decomposition to handle complex CDAGs.

Contribution

It develops an effective approach for composing lower bounds through graph decomposition and a static analysis algorithm for real-world program data access complexity.

Findings

Effective lower bounds for data access complexity derived

Graph decomposition improves analysis of complex CDAGs

Algorithm applicable to real programs with multiple sub-computations

Abstract

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. The problem of developing lower bounds for data access complexity has been modeled using the formalism of Hong & Kung's red/blue pebble game for computational directed acyclic graphs (CDAGs). However, previously developed approaches to lower bounds analysis for the red/blue pebble game are very limited in effectiveness when applied to CDAGs of real programs, with computations comprised of multiple sub-computations with differing DAG structure. We address this problem by developing an approach for effectively composing lower bounds based on graph decomposition. We also develop a static analysis algorithm to derive the asymptotic data-access lower bounds of programs, as a function of the problem size and cache size.