A new lower bound for tree-width using maximum cardinality search

SIAM Journal on Discrete Mathematics

Volumn 16, Issue 3, 2003, Pages 345-353

  Lucena, Brian ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Lower bound; Maximum cardinality search; Tree width; Triangulation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; MARKOV PROCESSES; THEOREM PROVING;

LOWER BOUND; MAXIMUM CARDINALITY SEARCH; TREE-WIDTH;

TREES (MATHEMATICS);

EID: 0042887143     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480101397773     Document Type: Article

References (12)

1. E. Amir, Efficient approximation for triangulation of minimum tree-width, in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, 2001.
2. S. Arnborg, Efficient algorithms for combinatorial graphs with bounded decomposability-A survey, BIT, 25 (1985), pp. 2-23.
3. S. Arnborg, D. G. Corneil, and A. Proskurowski, Complexity of finding embeddings in a k-tree, SIAM J. Alg. Disc. Meth., 8 (1987), pp. 277-284.
4. H. Bodlaender and D. Thilikos, Graphs with Branchwidth at Most Three, Technical report UU-CS-1997-37, Utrecht University, Department of Computer Science, Utrecht, The Netherlands, 1997.
5. S. Geman and K. Kochanek, Dynamic programming and the representation of soft-decodable codes, IEEE Trans. Inform. Theory, 47 (2001), pp. 549-568.
6. A. Koster, H. Bodlaender, and S. van Hoesel, Treewidth: Computational Experiments, Technical report 01-38, Konrad-Zuse-Zentrum fur Informationstechnik Berlin, Berlin, Germany, 2001.
7. S. Lauritzen and D. Speigelhalter, Local computations with probabilities on graphical structures and their application to expert systems, J. R. Stat. Soc. Ser. B Stat. Methodol., 50 (1988), pp. 157-224.
8. B. Lucena, Dynamic Programming, Tree-Width, and Computation on Graphical Models, Ph.D. thesis, Brown University, Providence, RI, 2002.
9. S. Ramachandramurthi, The structure and number of obstructions to treewidth, SIAM J. Discrete Math., 10 (1997), pp. 146-157.
10. B. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge, UK, 1996.
11. D. J. Rose, On simple characterizations of k-trees, Discrete Math., 7 (1974), pp. 317-322.
12. R. E. Tarjan and M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984), pp. 566-579.