Towards an automatic ordering for a symmetric sparse direct solver

In recent years, nested dissection has grown in popularity as the method of choice for computing a pivot sequence for use with a sparse direct symmetric solver. This is particularly true for very large problems. For smaller problems, minimum degree based algorithms often produce orderings that lead to sparser matrix factors. Furthermore, minimum degree orderings are frequently significantly cheaper to compute than nested dissection. In this report, we look at whether we can predict which ordering will be better, using only the sparsity pattern of the matrix. Our aim is to choose efficiently a good ordering for a wide range of large problems from different application areas.