Sparse Matrix Ordering Methods for Interior Point

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. This paper evaluates several methods for performing ll-reducing ordering on a variety of large-scale linear programming problems. We nd that a new method, based on the nested dissection heuristic, provides signiicantly better orderings than the most commonly used ordering method, minimum degree.