Abstract

The Minimum Degree Algorithm, one of the classical algorithms of sparse matrix computations, is a heuristic for computing a minimum triangulation of a graph. It is widely used as a component in every sparse matrix package, and it is known to produce triangulations with few fill edges in practice, although no theoretical bound or guarantee has been shown concerning the amount of fill it introduces. An additional remarkable property of Minimum Degree observed in practice is that it often produces a minimal triangulation. Despite extensive research on optimizing the running time of this heuristic, few theoretical results are known about it. Our goal

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