The Minimum Degree Ordering with Constraints

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 nested dissection. The minimum degree ordering is then applied subject to the constraint that the separator nodes must be ordered last. It is shown experimentally that the quality of the resulting ordering from this constrained scheme exhibits less sensitivity to the initial matrix ordering than that of the original minimum degree ordering. An important application of this approach to find orderings suitable for parallel elimination is also illustrated.