Algorithmic Aspects of Vertex Elimination on Graphs

@article{Rose1976AlgorithmicAO,
  title={Algorithmic Aspects of Vertex Elimination on Graphs},
  author={Donald J. Rose and Robert E. Tarjan and George S. Lueker},
  journal={SIAM J. Comput.},
  year={1976},
  volume={5},
  pages={266-283}
}
We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations. We give a new linear-time algorithm to calculate the fill-in produced by any elimination ordering, and we give two new related algorithms for finding orderings with special properties. One algorithm, based on breadth-first search, finds a perfect elimination ordering, if any exists, in $O(n + e)$ time, if the problem graph has n… 

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