Linearity of grid minors in treewidth with applications through bidimensionality

Combinatorica

Volumn 28, Issue 1, 2008, Pages 19-36

  Demaine, Erik D ^a   Hajiaghayi, Mohammadtaghi ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43049085522     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-008-2140-4     Document Type: Article

References (40)

1. 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 (2002), 461-493.
2. J. Alber, H. Fan, M. R. Fellows, H. Fernau, R. Niedermeier, F. A. Rosamond and U. Stege: A refined search tree technique for dominating set on planar graphs, Journal of Computer and System Sciences 71(4) (2005), 385-405.
3. J. Alber, H. Fernau and R. Niedermeier: Graph separators: a parameterized view; Journal of Computer and System Sciences 67 (2003), 808-832.
4. J. Alber, H. Fernau and R. Niedermeier: Parameterized complexity: exponential speed-up for planar graph problems; Journal of Algorithms 52 (2004), 26-56.
5. N. Alon, P. Seymour and R. Thomas: A separator theorem for nonplanar graphs, Journal of the American Mathematical Society 3 (1990), 801-808.
6. E. Amir: Efficient approximation for triangulation of minimum treewidth, in: Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), San Francisco, CA, 2001, Morgan Kaufmann Publishers, pp. 7-15.
7. B. S. Baker: Approximation algorithms for NP-complete problems on planar graphs, Journal of the Association for Computing Machinery 41 (1994), 153-180.
8. M.-S. Chang, T. Kloks and C.-M. Lee: Maximum clique transversals, in: Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2001), vol. 2204 of Lecture Notes in Computer Science, 2001, pp. 32-43.
9. C. Chekuri, S. Khanna and F. B. Shepherd: Edge-disjoint paths in planar graphs, in: Proceedings of the 45th Symposium on Foundations of Computer Science (FOCS 2004), 2004, pp. 71-80.
10. E. D. Demaine, F. V. Fomin, M. Hajiaghayi and D. M. Thilikos: Bidimensional parameters and local treewidth, SIAM Journal on Discrete Mathematics 18 (2004), 501-511.
11. E. D. Demaine, F. V. Fomin, M. Hajiaghayi and D. M. Thilikos: Fixed-parameter algorithms for (k,r)-center in planar graphs and map graphs, ACM Transactions on Algorithms 1 (2005), 33-47.
12. E. D. Demaine, F. V. Fomin, M. Hajiaghayi and D. M. Thilikos: Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs, Journal of the ACM 52 (2005), 866-893.
13. E. D. Demaine and M. Hajiaghayi: Diameter and treewidth in minor-closed graph families, revisited; Algorithmica 40(3) (2004), 211-215.
14. E. D. Demaine and M. 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), January 2004, pp. 833-842.
15. E. D. Demaine and M. 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, pp. 590-601.
16. E. D. Demaine and M. Hajiaghayi: Graphs excluding a fixed minor have grids as large as treewidth, with combinatorial and algorithmic applications through bidimensionality; in: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, January 2005, pp. 682-689.
17. E. D. Demaine, M. Hajiaghayi and K. Kawarabayashi: Algorithmic graph minor theory: Decomposition, approximation, and coloring; in: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, Pittsburgh, PA, October 2005, pp. 637-646.
18. E. D. Demaine, M. Hajiaghayi, N. Nishimura, P. Ragde and D. M. Thilikos: Approximation algorithms for classes of graphs excluding single-crossing graphs as minors, Journal of Computer and System Sciences 69 (2004), pp. 166-195.
19. E. D. Demaine, M. Hajiaghayi and D. M. Thilikos: The bidimensional theory of bounded-genus graphs, SIAM Journal on Discrete Mathematics 20(2) (2006), 357-371.
20. E. D. Demaine, M. Hajiaghayi and D. 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), Vol. 2462 of Lecture Notes in Computer Science, 2002, pp. 67-80.
21. E. D. Demaine, M. Hajiaghayi and D. M. Thilikos: Exponential speedup of fixed-parameter algorithms for classes of graphs excluding single-crossing graphs as minors, Algorithmica 41 (2005), 245-267.
22. R. Diestel, T. R. Jensen, K. Y. Gorbunov and C. Thomassen: Highly connected sets and the excluded grid theorem, Journal of Combinatorial Theory, Series B 75 (1999), 61-73.
23. D. Eppstein: Diameter and treewidth in minor-closed graph families, Algorithmica 27 (2000), 275-291.
24. U. Feige, M. Hajiaghayi and J. R. Lee: Improved approximation algorithms for minimum-weight vertex separators, in: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC 2005), Baltimore, May 2005, pp. 563-572.
25. F. V. Fomin and D. M. Thilikos: Dominating sets in planar graphs: Branch-width and exponential speed-up; in: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), 2003, pp. 168-177.
26. M. Frick and M. Grohe: Deciding first-order properties of locally tree-decomposable structures, Journal of the ACM 48 (2001), 1184-1206.
27. M. Grohe: Local tree-width, excluded minors, and approximation algorithms, Combinatorica 23(4) (2003), 613-632.
28. G. Gutin, T. Kloks and C. M. Lee: Kernels in planar digraphs, Journal of Computer and System Sciences 71(2) (2005), 174-184.
29. M. Hajiaghayi and N. 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), 2002, pp. 305-318.
30. I. Kanj and L. Perković: Improved parameterized algorithms for planar dominating set, in: Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science (MFCS 2002), vol. 2420 of Lecture Notes in Computer Science, 2002, pp. 399-410.
31. P. N. Klein, S. A. Plotkin and S. Rao: Excluded minors, network decomposition, and multicommodity flow; in: Proceedings of the 25th Annual ACM Symposium on Theory of Computing (STOC'93), 1993, pp. 682-690.
32. T. Kloks, C. M. Lee and J. 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 (WG 2002), vol. 2573 of Lecture Notes in Computer Science, 2002, pp. 282-295.
33. R. J. Lipton and R. E. Tarjan: Applications of a planar separator theorem, SIAM Journal on Computing 9 (1980), 615-627.
34. B. A. Reed: Tree width and tangles: a new connectivity measure and some applications; in: Surveys in combinatorics, 1997 (London), vol. 241 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 1997, pp. 87-162.
35. N. Robertson and P. D. Seymour: Graph minors. II. Algorithmic aspects of treewidth; Journal of Algorithms 7 (1986), 309-322.
36. N. Robertson and P. D. Seymour: Graph minors. V. Excluding a planar graph; Journal of Combinatorial Theory, Series B 41 (1986), 92-114.
37. N. Robertson and P. D. Seymour: Graph minors. XVI. Excluding a non-planar graph; Journal of Combinatorial Theory, Series B 89 (2003), 43-76.
38. N. Robertson, P. D. Seymour and R. Thomas: Quickly excluding a planar graph, Journal of Combinatorial Theory, Series B 62 (1994), 323-348.
39. P. D. Seymour: Personal communication, May 2004.
40. P. D. Seymour and R. Thomas: Call routing and the ratcatcher, Combinatorica 14(2) (1994), 217-241.