An object-oriented collection of minimum degree algorithms

Abstract

The multiple minimum degree (MMD) algorithm and its va- riants have enjoyed more than 20 years of research and progress in gene- rating fill-reducing orderings for sparse, symmetric, positive definite ma- trices. Although conceptually simple, effcient implementations of these algorithms are deceptively complex and highly specialized. In this case study, we present an object-oriented library that implements several recent minimum degree-like algorithms. We discuss how object- oriented design forces us to decompose these algorithms in a different manner than earlier codes and demonstrate how this impacts the flexi- bility and effciency of our C++ implementation. We compare the per- formance of our code against other implementations in C or Fortran.