Approximating the Bandwidth for Asteroidal Triple-Free Graphs

Journal of Algorithms

Volumn 32, Issue 1, 1999, Pages 41-57

  Kloks, Ton ^a   Kratsch, Dieter ^b   Müller, Haiko ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011423220     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.1998.0997     Document Type: Article

References (34)

1. S. Arnborg, D. G. Corneil, and A. Proskurowski, Complexity of finding embeddings in a k-tree, SIAM J. Algebraic Discrete Methods 8 (1987), 277-284.
2. S. F. Assmann, G. W. Peck, M. M. Sysło, and J. Zak, The bandwidth of caterpillars with hairs of length 1 and 2, SIAM J. Algebraic Discrete Methods 2 (1981), 387-393.
3. G. Blache, M. Karpinski, and J. Wirtgen, On approximation intractability of the band-width problem, in "Electronic Colloquium on Computational Complexity, 1998," Report No. 14.
4. H. Bodlaender, M. R. Fellows, and M. T. Hallet, Beyond NP-completeness for problems of bounded width: Hardness for the W hierarchy, in "Proceedings of the 26th Annual Symposium on the Theory of Computation, 1994," pp. 449-458.
5. J. A. Bondy and U. S. R. Murty, "Graph Theory with Applications," Macmillan, London, 1976.
6. P. Z. Chinn, J. Chvátalová, A. K. Dewdney, and N. E. Gibbs, The bandwidth problem for graphs and matrices - A survey, J. Graph Theory 6 (1982), 223-254.
7. D. G. Corneil, S. Olariu, and L. Stewart, Asteroidal triple-free graphs, SIAM J. Discrete Math. 10 (1997), 399-430.
8. D. G. Corneil, S. Olariu, and L. Stewart, A linear time algorithm to compute dominating pairs in asteroidal triple-free graphs, in "Proceedings of the 22nd International Colloquium on Automata, Languages and Programming," Lecture Notes in Computer Science, Vol. 944, pp. 292-302, Springer-Verlag, New York/Berlin, 1995.
9. E. Dahlhaus and M. Karpinski, An efficient parallel algorithm for the minimal elimination ordering (MEO) of an arbitrary graph, Theor. Comput. Sci. 134 (1994), 493-528.
10. J. Deogun and D. Kratsch, Diametral path graphs, in "Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science WG'95," Lecture Notes in Computer Science, Vol. 1017, pp. 344-357, Springer-Verlag, New York/Berlin, 1995.
11. G. A. Dirac, On rigid circuit graphs, Abh. Math. Sem. Univ. Hamburg 25 (1961), 71-76.
12. U. Feige, Approximating the bandwidth via volume respecting embeddings, in "Proceedings of the 30th Annual Symposium on the Theory of Computing, 1998."
13. C. Flotow, On powers of m-trapezoid graphs, Discrete Appl. Math. 63 (1995), 187-195.
14. M. R. Garey, R. L. Graham, D. S. Johnson, and D. E. Knuth, Complexity results for bandwidth minimization, SIAM J. Appl. Math. 34 (1978), 477-495.
15. M. C. Golumbic, "Algorithmic Graph Theory and Perfect Graphs," Academic Press, New York, 1980.
16. E. Gurari and I. H. Sudborough, Improved dynamic programming algorithms for the bandwidth minimization and the mincut linear arrangement problem, J. Algorithms 5 (1984), 531-546.
17. S. Jiang, The bandwidth problem and bandwidth of cographs, unpublished manuscript, 1992.
18. H. Kaplan and R. Shamir, Pathwidth, bandwidth and completion problems to proper interval graphs with small cliques, SIAM J. Computing 25 (1996), 540-561.
19. D. J. Kleitman and R. V. Vohra, Computing the bandwidth of interval graphs, SIAM J. Discrete Math. 3 (1990), 373-375.
20. T. Kloks, "Treewidth - Computations and Approximations," Lecture Notes in Computer Science, Vol. 842, Springer-Verlag, New York/Berlin, 1994.
21. T. Kloks, D. Kratsch, and H. Müller, "Approximating the Bandwidth for Asteroidal Triple-Free Graphs," Forschungsergebnisse Math/95/6, FSU Jena, Germany, 1995.
22. T. Kloks, D. Kratsch, and H. Müller, Bandwidth on chain graphs, Information Processing Letters 68 (1998), 313-315.
23. T. Kloks, D. Kratsch, and J. Spinrad, On treewidth and minimum fill-in of asteroidal triple-free graphs, Theoret. Comput. Sci. 175 (1997), 309-335.
24. R. Mahesh, C. P. Rangan, and A. Srinivasan, On finding the minimum bandwidth of interval graphs, Inform. and Comput. 95 (1991), 218-224.
25. R. M. McConnell and J. P. Spinrad, Linear time transitive orientation, in "Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997," pp. 19-25.
26. R. H. Möhring, Triangulating graphs without asteroidal triples, Discrete Appl. Math. 64 (1996), 281-287.
27. B. Monien, The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete, SIAM J. Algebraic Discrete Methods 7 (1986), 505-512.
28. T. Ohtsuki, A fast algorithm for finding an optimal ordering for vertex elimination on a graph, SIAM J. Comput. 5 (1976), 133-145.
29. C. H. Papadimitriou, The NP-completeness of the bandwidth minimization problem, Computing 16 (1976), 263-270.
30. A. Parra and P. Scheffler, Characterizations and algorithmic applications of chordal embeddings, Discrete Appl. Math. 79 (1997), 171-188.
31. G.W. Peck and A. Shastri, Bandwidth of theta graphs with short paths, Discrete Math. 103 (1992), 177-187.
32. D. J. Rose, R. E. Tarjan, and G. Lueker, Algorithmic aspects of vertex elimination of graphs, SIAM J. Comput. 5 (1976), 266-283.
33. A. P. Sprague, An O(n log n) algorithm for bandwidth of interval graphs, SIAM J. Discrete Math. 7 (1994), 213-220.
34. J. S. Turner, On the probable performance of heuristics for bandwidth minimization, SIAM J. Comput. 15 (1986), 561-580.