Graphs excluding a fixed minor have grids as large as treewidth, with combinatorial and algorithmic applications through bidimensionality

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2005, Pages 682-689

  Demaine, Erik D ^a   Hajiaghayi, MohammadTaghi ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; COMBINATORIAL MATHEMATICS; PARAMETER ESTIMATION; THEOREM PROVING; TREES (MATHEMATICS);

APPROXIMATION ALGORITHMS; BIDIMENSIONALITY THEORY; SEPARATOR THEOREMS; TREEWIDTH;

GRAPH THEORY;

EID: 20744453821     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (40)

1. [ABF+02] J. Alber, H. L. Bodlaender, H. Fernau, T. Kloks, and R. Niedermeier. Fixed parameter algorithms for dominating set and related problems on planar graphs. Algorithmica, 33(4):461-493, 2002.
2. [AFF+01] Jochen Alber, Hongbing Fan, Michael R. Fellows, Henning Fernau, Rolf Niedermeier, Frances A. Rosamond, and Ulrike Stege. Refined search tree technique for DOMINATING SET on planar graphs. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, volume 2136 of Lecture Notes in Computer Science, pages 111-122, 2001.
3. [AFN03] Jochen Alber, Henning Fernau, and Rolf Niedermeier. Graph separators: a parameterized view. Journal of Computer and System Sciences, 67(4):808-832, December 2003.
4. [AFN04] Jochen Alber, Henning Fernau, and Rolf Niedermeier. Parameterized complexity: exponential speed-up for planar graph problems. Journal of Algorithms, 52(1):26-56, 2004.
5. [Ami01] Eyal Amir. Efficient approximation for triangulation of minimum treewidth. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), pages 7-15, San Francisco, CA, 2001. Morgan Kaufmann Publishers.
6. [AST90] Noga Alon, Paul Seymour, and Robin Thomas. A separator theorem for nonplanar graphs. Journal of the American Mathematical Society, 3(4):801-808, 1990.
7. [Bak94] Brenda S. Baker. Approximation algorithms for NPcomplete problems on planar graphs. Journal of the Association for Computing Machinery, 41 (1): 153-180, 1994.
8. [CKL01] Maw-Shang Chang, Ton Kloks, and Chuan-Min Lee. Maximum clique transversals. In Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2001, Boltenhagen, Germany), volume 2204 of Lecture Notes in Computer Science, pages 32-43, Berlin, 2001. Springer.
9. [DFHT] Erik D. Demaine, Fedor V. Fomin, Mohammadtaghi Hajiaghayi, and Dimitrios M. Thilikos. Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs. ACM Transactions on Algorithms. To appear.
10. A preliminary version appears in Proceedings of the 30th International Colloquium on Automata, Languages and Programming, LNCS 2719, 2003, pages 829-844.
11. [DFHT04a] Erik D. Demaine, Fedor V. Fomin, Mohammadtaghi Hajiaghayi, and Dimitrios M. Thilikos. Bidimensional parameters and local treewidth. SIAM Journal on Discrete Mathematics, 2004. To appear.
12. A preliminary version appears in Proceedings of the 6th Latin American Symposium on Theoretical Informatics, LNCS 2976, 2004, pages 109-118.
13. [DFHT04b] Erik D. Demaine, Fedor V. Fomin, Mohammadtaghi Hajiaghayi, and Dimitrios M. Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs. In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA'04), pages 823-832, January 2004.
14. [DH04a] Erik D. Demaine and Mohammad Hajiaghayi. Equivalence of local treewidth and linear local treewidth and its algorithmic applications, In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA'04), pages 833-842, January 2004.
15. [DH04b] Erik D. Demaine and Mohammadtaghi Hajiaghayi. Diameter and treewidth in minor-closed graph families, revisited. Algorithmica, 40(3):211-215, August 2004.
16. [DH05] Erik D. Demaine and MohammadTaghi Hajiaghayi. Bidimensionality: New connections between FPT algorithms and PTASs. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, January 2005. To appear.
17. [DHN+04] Erik D. Demaine, Mohammadtaghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, and Dimitrios M. Thilikos. Approximation algorithms for classes of graphs excluding single-crossing graphs as minors. Journal of Computer and System Sciences, 69(2); 166-195, September 2004.
18. [DHT] Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos. Exponential speedup of fixed-parameter algorithms for classes of graphs excluding single-crossing graphs as minors. Algorithmica. To appear.
19. A preliminary version appears in Proceedings of the 13th Annual International Symposium on Algorithms and Computation Theoretical Informatics, LNCS 2518, 2002, pages 262-273.
20. [DHT02] Erik D. Demaine, Mohammadtaghi Hajiaghayi, and Dimitrios M. Thilikos. A 1.5-approximation for treewidth of graphs excluding a graph with one crossing. In Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization (Italy, APPROX 2002), volume 2462 of Lecture Notes in Computer Science, pages 67-80, 2002.
21. [DHT04] Erik D. Demaine, Mohammadtaghi Hajiaghayi, and Dimitrios M. Thilikos. The bidimensional theory of boundedgenus graphs. In Proceedings of the 29th International Symposium on Mathematical Foundations of Computer Science (MFCS 2004), pages 191-203, Prague, August 2004.
22. [DJGT99] Reinhard Diestel, Tommy R. Jensen, Konstantin Yu. Gorbunov, and Carsten Thomassen. Highly connected sets and the excluded grid theorem. Journal of Combinatorial Theory, Series B, 75(1):61-73, 1999.
23. [Epp00] David Eppstein. Diameter and treewidth in minor-closed graph families. Algorithmica, 27(3-4):275-291, 2000.
24. [FG01] Markus Frick and Martin Grohe. Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM, 48(6): 1184-1206, 2001.
25. [FT03] Fedor V. Fomin and Dimitiros M. Thilikos. Dominating sets in planar graphs: Branch-width and exponential speedup. In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 168-177, 2003.
26. [GKL01] Gregory Gutin, Ton Kloks, and C. M. Lee. Kernels in planar digraphs. In Optimization Online. Mathematical Programming Society, Philadelphia, 2001.
27. [Gro03] Martin Grohe. Local tree-width, excluded minors, and approximation algorithms. Combinatorica, 23(4):613-632, 2003.
28. [HN02] Mohammadtaghi Hajiaghayi and Naomi Nishimura. Subgraph isomorphism, log-bounded fragmentation and graphs of (locally) bounded treewidth. In Proc. the 27th International Symposium on Mathematical Foundations of Computer Science (Poland, 2002), pages 305-318, 2002.
29. [KLL02] Ton Kloks, C. M. Lee, and Jim Liu. New algorithms for k-face cover, k-feedback vertex set, and k-disjoint set on plane and planar graphs. In Proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science (WC 2002), volume 2573 of Lecture Notes in Computer Science, pages 282-295, 2002.
30. [KP02] Iyad Kanj and Ljubomir Perković. Improved parameterized algorithms for planar dominating set. In Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science, volume 2420 of Lecture Notes in Computer Science, pages 399-410. Springer, Lecture Notes in Computer Science, Berlin, vol.2420, 2002.
31. [LT80] Richard J. Lipton and Robert Endre Tarjan. Applications of a planar separator theorem. SIAM Journal on Computing, 9(3):615-627, 1980.
32. [Ree97] B. A. Reed. Tree width and tangles: a new connectivity measure and some applications. In Surveys in combinatorics, 1997 (London), volume 241 of London Math. Soc. Lecture Note Ser., pages 87-162. Cambridge Univ. Press, Cambridge, 1997.
33. [RS86a] Neil Robertson and P. D. Seymour. Graph minors. V. Excluding a planar graph. Journal of Combinatorial Theory, Series B, 41(1):92-114, 1986.
34. [RS86b] Neil Robertson and Paul D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7(3):309-322, 1986.
35. [RS91] Neil Robertson and P. D. Seymour. Graph minors. X. Obstructions to tree-decomposition. Journal of Combinatorial Theory, Series B, 52(2): 153-190, 1991.
36. [RS94] Neil Robertson and P. D. Seymour. Graph minors. XI. Circuits on a surface. Journal of Combinatorial Theory, Series B, 60(1):72-106, 1994.
37. [RS03] Neil Robertson and P. D. Seymour. Graph minors. XVI. Excluding a non-planar graph. Journal of Combinatorial Theory. Series B, 89(1):43-76, 2003.
38. [RST94] Neil Robertson, Paul D. Seymour, and Robin Thomas. Quickly excluding a planar graph. Journal of Combinatorial Theory, Series B, 62(2):323-348, 1994.
39. [Sey04] Paul D. Seymour. Personal communication, May 2004.
40. [ST94] Paul D. Seymour and Robin Thomas. Call routing and the ratcatcher. Combinatorica, 14(2):217-241, 1994.