On brambles, grid-like minors, and parameterized intractability of monadic second-order logic

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2010, Pages 354-364

  Kreutzer, Stephan ^a   Tazari, Siamak ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS; COMPUTER CIRCUITS; GRAPHIC METHODS; PARAMETERIZATION; POLYNOMIAL APPROXIMATION; TEMPORAL LOGIC;

BOUNDED TREEWIDTH; COURCELLE'S THEOREMS; EXPONENTIAL BOUNDS; LINEAR-TIME ALGORITHMS; MONADIC SECOND-ORDER LOGIC; PARAMETERIZED ALGORITHM; PARAMETERIZED PROBLEMS; POLYNOMIAL-TIME ALGORITHMS;

GRAPH THEORY;

EID: 77951678954     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973075.30     Document Type: Conference Paper

References (41)

1. H. Bodlaender, F. Fomin, D. Lokshtanov, E. Penninkx, S. Saurabh, and D. Thilikos. (Meta) kernelization. In FOCS '09: Proceedings of the 46th annual IEEE symposium on Foundations of Computer Science, 2009. to appear.
2. H. L. Bodlaender, J. R. Gilbert, H. Hafsteinsson, and T. Kloks. Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. J. Algorithms, 18(2):238-255, 1995.
3. H. L. Bodlaender, A. Grigoriev, and A. M. C. A. Koster. Treewidth lower bounds with brambles. In ESA '05: Proceedings of the 13th annual European Symposium on Algorithms, LNCS vol. 3669, pages 391-402. Springer, 2005.
4. B. Bollobás and A. Thomason. Proof of a conjecture of Mader, Erdös and Hajnal on topological complete subgraphs. Europ. J. Combinatorics, 19:883-887, 1998.
5. V. Chandrasekaran, N. Srebro, and P. Harsha. Complexity of inference in graphical models. In UAI '08, Proceedings of the 24th Conference in Uncertainty in Artificial Intelligence, pages 70-78. AUAI Press, 2008.
6. M. Chapelle, F. Mazoit, and I. Todinca. Constructing brambles. In MFCS 09': Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science, LNCS vol. 5734, pages 223-234. Springer, 2009.
7. B. Courcelle. Graph rewriting: An algebraic and logic approach. In Handbook of Theoretical Computer Science, volume 2, pages 194-242. Elsevier, 1990.
8. A. Dawar, M. Grohe, and S. Kreutzer. Locally excluding a minor. In LICS '07: Proceedings of the 22nd annual IEEE symposium on Logic in Computer Science, pages 270-279. IEEE press, 2007.
9. A. Dawar, M. Grohe, S. Kreutzer, and N. Schweikardt. Approximation schemes for first-order definable optimisation problems. In LICS '06: Proceedings of the 21st annual IEEE symposium on Logic in Computer Science, pages 411-420. IEEE press, 2006.
10. E. D. Demaine, F. V. Fomin, M. Hajiaghayi, and D. M. Thilikos. Bidimensional parameters and local treewidth. SIAM J. Discret Math., 18(3):501-511, 2005.
11. E. D. Demaine and M. T. Hajiaghayi. Quickly deciding minor-closed parameters in general graphs. Eur. J. Comb., 28(1):311-314, 2007.
12. R. Diestel. Graph Theory. Springer, 2005.
13. R. Diestel, K. Gorbunov, T. Jensen, and C. Thomassen. Highly connected sets and the excluded grid theorem. J. Comb. Theory, Ser. B, 75:61-73, 1999.
14. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer-Verlag, 1999.
15. D. Eppstein. Diameter and treewidth in minor-closed graph families. Algorithmica, 27(3):275-291, 2000.
16. P. Erdös and L. Lovász. Problems and results on 3-chormatic hypergraphs and some related questions. In Infinite and Finite Sets, volume 10 of Colloq. Math. Soc. János Bolyai, pages 609-627. North-Holland, 1975.
17. U. Feige, M. Hajiaghayi, and J. R. Lee. Improved approximation algorithms for minimum weight vertex separators. SIAM J. Comput., 38(2):629-657, 2008.
18. M. R. Fellows and M. A. Langston. Nonconstructive tools for proving polynomial-time decidability. J. ACM, 35(3):727-739, 1988.
19. J. Flum and M. Grohe. Fixed-parameter tractability, definability, and model-checking. SIAM J. Comput., 31(1):113-145, 2001.
20. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer, 2006. ISBN 3-54-029952-1.
21. M. Frick and M. Grohe. Deciding first-order properties of locally tree-decomposable structures. J. ACM, 48(6):1184-1206, 2001.
22. M. Grohe. Computing crossing numbers in quadratic time. J. Comput. Syst. Sci., 68(2):285-302, 2004.
23. M. Grohe. The complexity of homomorphism and constraint satisfaction problems seen from the other side. J. ACM, 54(1), 2007.
24. M. Grohe. Logic, graphs, and algorithms. In Logic and Automata - History and Perspectives, pages 357-422. Amsterdam University Press, 2007.
25. M. Grohe and D. Marx. On tree width, bramble size, and expansion. J. Comb. Theory, Ser. B, 99(1):218-228, 2009.
26. S. Kreutzer. On the parameterised intractability of monadic second-order logic. In CSL '09: Proceedings of the 18th annual conference on Computer Science Logic, LNCS vol. 5771, pages 348-363. Springer, 2009.
27. S. Kreutzer and S. Tazari. On brambles, grid-like minors, and parameterized intractability of monadic second-order logic. Available at arXiv:abs/0907.3076 [cs.DM], 2009.
28. F. T. Leighton and S. Rao. An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In FOCS '88: Proceedings of the 29th annual IEEE symposium on Foundations of Computer Science, pages 422-431. IEEE press, 1988.
29. L. Libkin. Elements of Finite Model Theory. Springer, 2004.
30. R. A. Moser. A constructive proof of the Lovász Local Lemma. In STOC '09: Proceedings of the 41st annual ACM Symposium on Theory of Computing, pages 343-350, New York, NY, USA, 2009. ACM.
31. R. A. Moser and G. Tardos. A constructive proof of the general Lovász Local Lemma. Available at arXiv:0903.0544v3 [cs.DS], 2009.
32. B. Reed. Finding approximate separators and computing tree width quickly. In STOC '92: Proceedings of the 24th annual ACM Symposium on Theory of Computing, pages 221-228, New York, NY, USA, 1992. ACM.
33. B. Reed. Tree Width and Tangles: A New Connectivity Measure And Some Applications. Survey in Combinatorics, 241:87-158, 1997.
34. B. Reed and D. R. Wood. Polynomial treewidth forces a large grid-like minor. Available at arXiv:0809.0724v3 [math.CO], 2008.
35. N. Robertson, P. Seymour, and R. Thomas. Quickly excluding a planar graph. J. Comb. Theory, Ser. B, 62(2):323-348, 1994.
36. N. Robertson and P. D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7(3):309-322, 1986.
37. N. Robertson and P. D. Seymour. Graph minors. V. Excluding a planar graph. J. Comb. Theory, Ser. B, 41(1):92-114, 1986.
38. N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Comb. Theory, Ser. B, 63(1):65-110, 1995.
39. N. Robertson and P. D. Seymour. Graph minors. XX. Wagner's conjecture. J. Comb. Theory, Ser. B, 92(2):325-357, 2004.
40. P. D. Seymour and R. Thomas. Graph searching and a min-max theorem for tree-width. J. Comb. Theory, Ser. B, 58(1):22-33, 1993.
41. A. Thomason. The extremal function for complete minors. J. Comb. Theory, Ser. B, 81(2):318-338, 2001.