An Approximate Minimum Degree Ordering Algorithm

An Approximate Minimum Degree ordering algorithm (AMD) 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 computationally cheap bounds for the minimum degree. We show that these bounds are often equal to the actual degree. The resulting algorithm is typically much faster than previous minimum degree ordering algorithms, and produces results that are comparable in quality with the best orderings from other minimum degree algorithms. ENSEEIHT-IRIT, Toulouse, France. email: [email protected]. Computer and Information Sciences Department University of Florida, Gainesville, Florida, USA. phone: (904) 392-1481, email: [email protected]. Technical reports and matrices are available via the World Wide Web at http://www.cis.ufl.edu/̃ davis, or by anonymous ftp at ftp.cis.ufl.edu:cis/tech-reports. Support for this project was provided by the National Science Foundation (ASC-9111263 and DMS-9223088). Portions of this work were supported by a post-doctoral grant from CERFACS. Rutherford Appleton Laboratory, Chilton, Didcot, Oxon. 0X11 0QX England, and European Center for Research and Advanced Training in Scientific Computation (CERFACS), Toulouse, France. email: [email protected]. Technical reports, information on the Harwell Subroutine Library, and matrices are available via the World Wide Web at http://www.cis.rl.ac.uk/struct/ARCD/NUM.html, or by anonymous ftp at seamus.cc.rl.ac.uk/pub.