It is well known that sparse matrix factorizations suffer fill. That is, some of the zero entries in a sparse matrix will become nonzero during factorization. To reduce factorization time and storage, it is important to arrange the computation so that the amount of fill is kept small. It is also well known that the amount of fill is often influenced greatly by how the rows and columns of the sp...

In this paper we consider a two-stage ordering problem with a buyer’s minimum commitment quantity contract. Under the contract the buyer is required to give a minimum-commitment quantity. Then the manufacturer has the obligations to supply the minimum-commitment quantity and to provide a shortage compensation policy to the buyer. We formulate a dynamic optimization model to determine the manufa...

AMD is a set of routines for permuting sparse matrices prior to numerical factorization, using the approximate minimum degree ordering algorithm. There are versions written in both C and Fortran 77. A MATLAB interface is included.

Recently proposed methods for ordering sparse symmetric matrices are discussed and their performance is compared with that of the Minimum Degree and the Minimum Local Fill algorithms. It is shown that these methods applied to symmetrized modified nodal analysis matrices yield orderings significantly better than those obtained from the Minimum Degree and Minimum Local Fill algorithms, in some ca...

Minimum degree and nested dissection are the two most popular reordering schemes used to reduce ll-in and operation count when factoring and solving sparse matrices. Most of the state-of-the-art ordering packages hybridize these methods by performing incomplete nested dissection and ordering by minimum degree the subgraphs associated with the leaves of the separation tree, but most often only l...

A classical theorem of Dirac states that every graph on n vertices with minimum degree at least n/2 contains a Hamilton cycle. If one seeks an analogue of this result for uniform hypergraphs, then several alternatives suggest themselves. In the following, we will restrict ourselves to 3-uniform hypergraphs H. Thus each hyperedge of H consists of precisely 3 vertices. A natural way to extend the...

A classic result of G. A. Dirac in graph theory asserts that every n-vertex graph (n ≥ 3) with minimum degree at least n/2 contains a spanning (so-called Hamilton) cycle. G. Y. Katona and H. A. Kierstead suggested a possible extension of this result for k-uniform hypergraphs. There a Hamilton cycle of an n-vertex hypergraph corresponds to an ordering of the vertices such that every k consecutiv...

The adjacency matrix is the most fundamental and intuitive object in graph analysis that useful not only mathematically but also for visualizing structures of graphs. Because appearance an critically affected by ordering rows columns, or vertex ordering, statistical assessment graphs together with their sequences important identifying characteristic In this paper, we propose a hypothesis testin...

In random geometric graphs, vertices are randomly distributed on [0, 1] and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cu...

The elimination tree is a rooted tree that is computed from the adjacency graph of a symmetric matrix A. The height of the elimination tree is one restricting factor when solving a sparse linear system Ax = b on a parallel computer using Cholesky factorization. An eecient algorithm is presented for the problem of ordering the nodes in a tree G so that its elimination tree is of minimum height. ...