Chordal deletion is fixed-parameter tractable

Algorithmica (New York)

Volumn 57, Issue 4, 2010, Pages 747-768

  Marx, Dániel ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Chordal deletion; Chordal graphs; Fixed parameter tractability

Indexed keywords

CHORDAL GRAPHS; FIXED-PARAMETER TRACTABILITY; NP-HARD; PARAMETERIZED; POLYNOMIAL-TIME ALGORITHMS; RUNNING TIME;

EID: 77952099143     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-008-9233-8     Document Type: Article

References (27)

1. Adler, I. Grohe, M. Kreutzer, S.: Computing excluded minors. In: SODA '08: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 641-650. Society for Industrial and Applied Mathematics, Philadelphia (2008)
2. H.L. Bodlaender 1993 A tourist guide through treewidth Acta Cybern. 11 1-2 1 21 0804.68101 1268488
3. L. Cai 1996 Fixed-parameter tractability of graph modification problems for hereditary properties Inf. Process. Lett. 58 4 171 176 0875.68702 10.1016/0020-0190(96)00050-6 (Pubitemid 126374630)
4. L. Cai 2003 Parameterized complexity of vertex colouring Discrete Appl. Math. 127 415 429 1015.05027 10.1016/S0166-218X(02)00242-1 1976024
5. Courcelle, B.: Graph rewriting: an algebraic and logic approach. In: Handbook of Theoretical Computer Science, vol. B, pp. 193-242. Elsevier, Amsterdam (1990)
6. 3) FPT algorithm for the undirected feedback vertex set problem Theory Comput. Syst. 41 3 479 492 1148.68037 10.1007/s00224-007- 1345-z 2352543 (Pubitemid 41450263)
7. Dom, M. Guo, J. Hüffner, F. Niedermeier, R. Tru, A.: Fixed-parameter tractability results for feedback set problems in tournaments. In: Algorithms and Complexity. Lecture Notes in Computer Science, vol. 3998, pp. 320-331. Springer, Berlin (2006) (Pubitemid 44071036)
8. Downey, R.G. Fellows, M.R.: Parameterized Complexity. Monographs in Computer Science. Springer, New York (1999)
9. Flum, J. Grohe, M.: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2006)
10. T. Gallai 1961 Maximum-minimum Sätze und verallgemeinerte Faktoren von Graphen Acta Math. Acad. Sci. Hung. 12 131 173 0142.41404 10.1007/BF02066678 130188
11. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)
12. M. Grohe 2004 Computing crossing numbers in quadratic time J. Comput. Syst. Sci. 68 2 285 302 1073.68064 10.1016/j.jcss.2003.07.008 2059096 (Pubitemid 32865737)
13. J. Guo J. Gramm F. Hüffner R. Niedermeier S. Wernicke 2006 Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization J. Comput. Syst. Sci. 72 8 1386 1396 1119.68134 10.1016/j.jcss.2006.02.001 (Pubitemid 44647241)
14. Heggernes, P. Paul, C. Telle, J.A. Villanger, Y.: Interval completion with few edges. In: STOC '07: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, pp. 374-381. ACM, New York (2007) (Pubitemid 47630756)
15. Ho, M.L.: Linear time algorithms for graphs close to chordal graphs. M. Phil. Thesis, Department of Computer Science and Engineering, The Chinese University of Hong Kong (2003)
16. H. Kaplan R. Shamir R.E. Tarjan 1999 Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs SIAM J. Comput. 28 5 1906 1922 0928.68124 10.1137/S0097539796303044 1694136 (Pubitemid 129304156)
17. J. Kleinberg 2003 Detecting a network failure Internet Math. 1 1 37 55 1087.94543 2076726 (Pubitemid 32075894)
18. Kloks, T.: Treewidth. Lecture Notes in Computer Science, vol. 842. Springer, Berlin (1994)
19. J.M. Lewis M. Yannakakis 1980 The node-deletion problem for hereditary properties is NP-complete J. Comput. Syst. Sci. 20 2 219 230 0436.68029 10.1016/0022-0000(80)90060-4 574592 (Pubitemid 11421552)
20. Lokshtanov, D.: Wheel-free deletion is W[2]-hard. In: Proceedings of the International Workshop on Parameterized and Exact Computation (IWPEC 2008). Lecture Notes in Computer Science, vol. 5018, pp. 141-147. Springer, Berlin (2008) (Pubitemid 351775566)
21. D. Marx 2006 Parameterized coloring problems on chordal graphs Theor. Comput. Sci. 351 3 407 424 1087.68072 10.1016/j.tcs.2005.10.008 2202499 (Pubitemid 43207634)
22. Marx, D. Schlotter, I.: Obtaining a planar graph by vertex deletion. In: 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2007). Lecture Notes in Computer Science, vol. 4769, pp. 292-303. Springer, Berlin (2007) (Pubitemid 351152844)
23. A. Natanzon R. Shamir R. Sharan 2001 Complexity classification of some edge modification problems Discrete Appl. Math. 113 1 109 128 0982.68104 10.1016/S0166-218X(00)00391-7 1855517 (Pubitemid 33732132)
24. B. Reed K. Smith A. Vetta 2004 Finding odd cycle transversals Oper. Res. Lett. 32 4 299 301 1052.05061 10.1016/j.orl.2003.10.009 2057781
25. N. Robertson P.D. Seymour 1995 Graph minors, XIII: the disjoint paths problem J. Comb. Theory Ser. B 63 1 65 110 0823.05038 10.1006/jctb.1995.1006 1309358
26. D.J. Rose R.E. Tarjan G.S. Lueker 1976 Algorithmic aspects of vertex elimination on graphs SIAM J. Comput. 5 2 266 283 0353.65019 10.1137/0205021 408312
27. M. Yannakakis 1981 Computing the minimum fill-in is NP-complete SIAM J. Algebr. Discrete Methods 2 1 77 79 0496.68033 10.1137/0602010 604513