Computing the Minimum Fill-in is NP^Complete

@article{Yannakakis1981ComputingTM,
  title={Computing the Minimum Fill-in is NP^Complete},
  author={Mihalis Yannakakis},
  journal={Siam Journal on Algebraic and Discrete Methods},
  year={1981},
  volume={2},
  pages={77-79}
}
  • M. Yannakakis
  • Published 1 March 1981
  • Computer Science, Mathematics
  • Siam Journal on Algebraic and Discrete Methods
We show that the following problem is NP-complete. Given a graph, find the minimum number of edges (fill-in) whose addition makes the graph chordal. This problem arises in the solution of sparse symmetric positive definite systems of linear equations by Gaussian elimination. 
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