# 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.
768 Citations
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