A graph-based approach to map matrix algorithms onto local-access processor arrays

Abstract

The authors describe the application of the multi-mesh graph (MMG) method to the mapping of large matrix algorithms onto class-specific local-access processor arrays. These arrays consist of cells with large local memory (i.e., memory size proportional to the size of the problems) and low cell bandwidth (much smaller than the cell computation rate). The results given indicate that the MMG method allows the analysis of such issues as allocation operations to cells, load balancing, scheduling, synchronization, and overhead in computations and data transfers. These aspects are illustrated by mapping the LU-decomposition algorithm onto a linear memory-linked array. Performance estimates indicate that mapping with the MMG method produces 94% utilization of cells in the target structure used. Therefore, the MMG is a suitable tool for mapping matrix algorithms onto pre-existing arrays.<>