Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization

This paper discusses a hypergraph-based unsymmetric nested dissection (HUND) ordering for reducing the fill-in incurred during Gaussian elimination. The usage of hypergraphs in the paper's approach is fairly standard, and HUND can be implemented by calling an existing hypergraph partitioner that uses recursive bisection. The paper's implementation uses local reordering constrained column approximate minimum degree to further improve the ordering. The paper also explains how weighted matching (HSL routine MC64) can be used in this context. Experimental results on 27 medium and large size matrices with highly unsymmetric structures compare the paper's approach to four other wellknown reordering algorithms. The results show that it provides a robust reordering algorithm, in the sense that it is the best or close to the best (often within 10%) of all the other methods, in particular on matrices with highly unsymmetric structures.