Simple and efficient modifications of elimination orderings

Authors:
Pinar Heggernes;Yngve Villanger
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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Abstract

We study the problem of modifying a given elimination ordering through local reorderings. We present new theoretical results on equivalent orderings, including a new characterization of such orderings. Based on these results, we define the notion of k-optimality for an elimination ordering, and we describe how to use this in a practical context to modify a given elimination ordering to obtain less fill. We experiment with different values of k, and report on percentage of fill that is actually reduced from an already good initial ordering, like Minimum Degree.