Scalability of sparse Cholesky factorization

A variety of algorithms have been proposed for sparse Cholesky factorization, including left-looking, right-looking, and supernodal algorithms. This article investigates shared-memory implementations of several variants of these algorithms in a task-oriented execution model with dynamic scheduling. In particular, we consider the degree of parallelism, the scalability, and the scheduling overhead of the different algorithms. Our emphasis lies in the parallel implementation for relatively large numbers of processors. As execution platform, we use the SB-PRAM, a shared-memory machine with up to 2048 processors. This article can be considered as a case study in which we try to answer the question of which performance we can hope to get for a typical irregular application on an ideal machine on which the locality of memory accesses can be ignored but for which the overhead for the management of data structures still takes effect. The investigation shows that certain algorithms are the best choice for a small number of processors, while other algorithms are better for many processors.