The evolution of the minimum degree ordering algorithm

Chetwynd and Hilton showed that any regular graph G of even order n which has relatively high degree $\Delta (G)\,\ge\,((\sqrt{7}- 1)/2)\, n$ has a 1-factorization. This is equivalent to saying that under these conditions G has chromatic index equal to ...

An approximate minimum degree (AMD) ordering algorithm for preordering a symmetric sparse matrix prior to numerical factorization is presented. We use techniques based on the quotient graph for matrix factorization that allow us to obtain ...

A hybrid scheme for ordering sparse symmetric matrices is considered. It is based on a combined use of the top-down nested dissection and the bottom-up minimum degree ordering schemes. A separator set is first determined by some form of incomplete ...