Solving Alignment using Elementary Linear Algebra

Abstract

Data and computation alignment is an important part of compiling sequential programs to architectures with non-uniform memory access times. In this paper, we show that elementary matrix methods can be used to determine communication-free alignment of code and data. We also solve the problem of replicating read-only data to eliminate communication. Our matrix-based approach leads to algorithms which are simpler and faster than existing algorithms for the alignment problem.