Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …

The subject of sparse matrices has its root in such diverse fields as management science,
power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of …

Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite
optimization problems and in related convex optimization problems involving sparse positive …

For more and more applications, it is important to be able to compute the treewidth of a given
graph and to find tree decompositions of small width reasonably fast. This paper gives an …

Any given graph can be embedded in a chordal graph by adding edges, and the resulting
chordal graph is called a triangulation of the input graph. In this paper we study minimal …

We present a new algorithm, called MCS-M, for computing minimal triangulations of graphs.
Lex-BFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other …

Contraction hierarchies are a speed-up technique to improve the performance of shortest-
path computations, which works very well in practice. Despite convincing practical results …

Abstract The Minimum Degree Algorithm, one of the classical algorithms of sparse matrix
computations, is a heuristic for computing a minimum triangulation of a graph. It is widely …

We present a new algorithm, called LB-Triang, which computes minimal triangulations. We
give both a straightforward O (nm′) time implementation and a more involved O (nm) time …

The Mayer sampling method was used to compute the virial coefficients of high-dimensional
hard-sphere fluids. The first 64 virial coefficients for dimensions 12< D⩽ 100 were obtained …