Improved load distribution in parallel sparse Cholesky factorization

Abstract

Compared to the customary column-oriented approaches, block-oriented, distributed-memory sparse Cholesky factorization benefits from an asymptotic reduction in interprocessor communication volume and an asymptotic increase in the amount of concurrency that is exposed in the problem. Unfortunately, block-oriented approaches (specifically, the block fan-out method) have suffered from poor balance of the computational load. As a result, achieved performance can be quite low. This paper investigates the reasons for this load imbalance and proposes simple block mapping heuristics that dramatically improve it. The result is a roughly 20% increase in realized parallel factorization performance, as demonstrated by performance results from an Intel Paragon system. We have achieved performance of nearly 3.2 billion floating point operations per second with this technique on a 196-node Paragon system.