The bidimensional theory of bounded-genus graphs

SIAM Journal on Discrete Mathematics

Volumn 20, Issue 2, 2006, Pages 357-371

  Demaine, Erik D ^a   Hajiaghayi, Mohammadtaghi ^a   Thilikos, Dimitrios M ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

Graph contractions; Graph minors; Graphs on surfaces; Grids; Treewidth

Indexed keywords

GRAPH CONTRACTIONS; GRAPH MINORS; GRAPHS ON SURFACES;

ALGORITHMS; BOUNDARY CONDITIONS; COMBINATORIAL OPTIMIZATION; GRAPH THEORY;

PROBLEM SOLVING;

EID: 34249062041     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/040616929     Document Type: Article

References (31)

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), pp. 461-493.
2. J. ALBER, H. FAN, M. R. FELLOWS, H. FERNAU, R. NIEDERMEIER, F. 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 (MFCS 2001), Lecture Notes in Comput. Sci. 2136, Springer-Verlag, Berlin, 2001, pp. 111-122.
3. J. ALBER, H. FERNAU, AND R. NIEDERMEIER, Parameterized complexity: Exponential speed-up for planar graph problems, J. Algorithms, 52 (2004), pp. 26-56.
4. E. AMIR, Efficient approximation for triangulation of minimum treewidth, in Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), Morgan Kaufmann, San Francisco, 2001, pp. 7-15.
5. 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), Lecture Notes in Comput. Sci. 2204, Springer-Verlag, Berlin, 2001, pp. 32-43.
6. R. G. DOWNEY AND M. R. FELLOWS, Parameterized Complexity, Springer-Verlag, New York, 1999.
7. E. D. DEMAINE, F. V. FOMIN, M. HAJIAGHAYI, AND D. M. THILIKOS, Bidimensional parameters and local treewidth, SIAM 3. Discrete Math., 18 (2004), pp. 501-511.
8. 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, in Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), New Orleans, 2004, pp. 823-832.
9. E. D. DEMAINE, F. V. FOMIN, M. HAJIAGHAYI, AND D. M. THILIKOS, Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs, ACM Trans. Algorithms, 1 (2005), pp. 33-47.
10. E. D. DEMAINE AND M. HAJIAGHAYI, Diameter and treewidth in minor-closed graph families, revisited, Algorithmica, 40 (2004), pp. 211-215.
11. 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 2004), New Orleans, 2004, pp. 833-842.
12. E. D. DEMAINE AND M. HAJIAGHAYI, Fast algorithms for hard graph problems: Bidimensionality, minors, and local treewidth, in Proceedings of the 12th International Symposium on Graph Drawing (Harlem, NY, 2004), Lecture Notes in Comput. Sci. 3383, Springer-Verlag, Berlin, 2004, pp. 517-533.
13. 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, 2005, pp. 590-601.
14. 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, 2005, pp. 682-689.
15. 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, J. Comput. System Sci., 69 (2004), pp. 166-195.
16. 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), pp. 245-267.
17. 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), Baltimore, 2003, pp. 168-177.
18. G. GUTIN, T. KLOKS, C. M. LEE, AND A. YEO, Kernels in planar digraphs, J. Comput. System Sci., 71 (2005), pp. 174-184.
19. 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), Lecture Notes in Comput. Sci. 2573, Springer-Verlag, Berlin, 2002, pp. 282-295.
20. 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, Lecture Notes in Comput. Sci. 2420, Springer-Verlag, 2002, pp. 399-410.
21. J. LAGERGREN, Efficient parallel algorithms for graphs of bounded tree-width, J. Algorithms, 20 (1996), pp. 20-44.
22. L. LOVÁSZ, Private communication, 2003.
23. B. MOHAR AND C. THOMASSEN, Graphs on Surfaces, Johns Hopkins Stud. Math. Sci., The Johns Hopkins University Press, Baltimore, MD, 2001.
24. B. A. REED, Finding approximate separators and computing tree width quickly, in Proceedings of the 24th Annual ACM Symposium on Theory of Computing (STOC 1992), ACM, New York, 1992, pp. 221-228.
25. N. ROBERTSON AND P. D. SEYMOUR, Graph minors -a survey, in Surveys in Combinatorics, I. Anderson, ed., Cambridge University Press, Cambridge, UK, 1985, pp. 153-171.
26. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. II. Algorithmic aspects of tree-width, J. Algorithms, 7 (1986), pp. 309-322.
27. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. VII. Disjoint paths on a surface, J. Combin. Theory Ser. B, 45 (1988), pp. 212-254.
28. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. X. Obstructions to tree-decomposition, J. Combin. Theory Ser. B, 52 (1991), pp. 153-190.
29. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. XIII. The disjoint paths problem, J. Combin. Theory Ser. B, 63 (1995), pp. 65-110.
30. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. XVI. Excluding a non-planar graph, J. Combin. Theory Ser. B, 89 (2003), pp. 43-76.
31. N. ROBERTSON, P. D. SEYMOUR, AND R. THOMAS, Quickly excluding a planar graph, J. Combin. Theory Ser. B, 62 (1994), pp. 323-348.