Making an arbitrary filled graph minimal by removing fill edges

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1097, Issue , 1996, Pages 173-184

  Blair, Jean R S ^a   Heggernes, Pinar ^b   Telle, Jan Arne ^b  

^a UNITED STATES MILITARY ACADEMY   (United States)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH G; GREEDY STRATEGIES; MINIMAL ELIMINATION ORDERING; REVERSE ORDER; RUNTIMES; SUPERGRAPH;

GRAPH THEORY;

EID: 84947934438     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61422-2_130     Document Type: Conference Paper

References (15)

1. A. Agrawal, P. Klein, and R. Ravi. Cutting down on fill using nested dissection: provably good elimination orderings. In J. A. George, J. R. Gilbert, and J. W. H. Liu, editors, Sparse matrix computations: Graph theory issues and algorithms, pages 31-55. Springer Vedag, 1993. IMA Volumes in Mathematics and its Applications, Vol. 56.
2. C. Beeri, R. Fagin, D. Maier, and M. Yannakakis. On the desirability of acyclic database systems. J. Assoc. Comput. Much., 30:479-513, 1983.
3. F. R. K. Chung and D. Mumford. Chordal completions of planar graphs. J. Comb. Theory, 31:96-106, 1994.
4. E. Dahlhaus and M. Karpinski. An efficient parallel algorithm for the minimal elimination ordering of an arbitrary graph. Proceedings FOCS, pages 454-459, 1989.
5. R. E. England, J. R. S. Blair, and M. G. Thomason. Independent computations in a probablistic knowledge-based system. Technical Report CS-90-128, Department of Computer Science, The University of Tennessee, Knoxville, Tennessee, 1991.
6. A. George and J.W-H. Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1981.
7. S. L. Lauritzen and D. J. Spiegelhalter. Local computations with probabilities on graphical structures and their applications to expert systems. J. Royal Statist. Sac., set B, 50:157-224, 1988.
8. J. G. Lewis, B. W. Peyton, and A. Pothen. A fast algorithm for reordering sparse matrices for parallel factorization. SIAM J. Sci. Slat. Comput., 10:1156-1173, 1989.
9. J. W-H. Liu and A. Mirzaian. A linear reordering algorithm for parallel pivoting of chordal graphs. SIAM J. Disc. Math., 2:100-107, 1989.
10. T. Ohtsuki, L.K. Cheung, and T. Fujisawa. Minimal triangulation of a graph and optimal pivoting ordering in a sparse matrix. J. Math. Anal. Appl., 54:622-633, 1976.
11. B. W. Peyton. Some applications of clique trees to the solution of sparse linear systems. PhD thesis, Dept. of Mathematical Sciences, Clemson University, 1986.
12. D. J. Rose. A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations. In R. C. Read, editor, Graph Theory and Computing, pages 183-217. Academic Press, 1972.
13. D.J. Rose, R.E. Tarjan, and G.S. Lueker. Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput., 5:266-283, 1976.
14. R. E. Tarjan and M. Yannakalds. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput., 13:566-579, 1984.
15. M. Yannakakis. Computing the minimum fill-in is NP-complete. SIAM J. Alg. Disc. Meth., 2:77-79, 1981.