Solving Alignment using Elementary Linear Algebra

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. 1 Introduction: A key problem in generating code for non-uniform memory access (NUMA) parallel machines is data and computation placement --- that is, determining what work each processor must do, and what data must reside in each local memory. The goal of placement is to exploit parallelism by spreading the work across the processors, and to exploit locality by spreading data so that memory accesses are local whenever possible. The problem of determining a good placement for a program is usually solved in two phases called alignment and distribution