论文信息 - Computing the Minimum Fill-in is NP^Complete

Computing the Minimum Fill-in is NP^Complete

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.

M. Yannakakis

[1] D. Rose. A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS , 1972 .

[2] D. Rose,et al. Algorithmic aspects of vertex elimination on directed graphs. , 1975 .

[3] Robert E. Tarjan,et al. Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[4] David S. Johnson,et al. Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[5] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6] Mihalis Yannakakis,et al. Node-Deletion Problems on Bipartite Graphs , 1981, SIAM J. Comput..