Generic Graph Algorithms for Sparse Matrix Ordering

Fill-reducing sparse matrix orderings have been a topic of active research for many years. Although most such algorithms are developed and analyzed within a graph-theoretical framework, for reasons of performance the corresponding implementations are typically realized with programming languages devoid of language features necessary to explicitly represent graph abstractions. Recently, generic programming has emerged as a programming paradigm capable of providing high levels of performance in the presence of programming abstractions. In this paper we present an implementation of the Minimum Degree ordering algorithm using the newly-developed Generic Graph Component Library. Experimental comparisons show that, despite our heavy use of abstractions, our implementation has performance indistinguishable from that of a widely used Fortran implementation.