New upper bounds on the decomposability of planar graphs

Journal of Graph Theory

Volumn 51, Issue 1, 2006, Pages 53-81

  Fomin, Fedor V ^a   Thilikos, Dimitrios M ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

Branch width; Parameterized algorithms; Planar graphs; Separation theorems; Subexponential algorithms; Tree width

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; TREES (MATHEMATICS);

BRANCH WIDTH; PARAMETERIZED ALGORITHMS; PLANAR GRAPHS; SEPARATION THEOREMS; SUBEXPONENTIAL ALGORITHMS; TREE WIDTH;

GRAPH THEORY;

EID: 33645293145     PISSN: 03649024     EISSN: 10970118     Source Type: Journal    
DOI: 10.1002/jgt.20121     Document Type: Article

References (23)

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, M. R. Fellows, and R. Niedermeier, Polynomial-time data reduction for dominating set, J ACM 51 (2004), 363-384.
3. J. Alber, H. Fernau, and R. Niedermeier, Graph separators: A parameterized view, J Comput System Sci 67 (2003), 808-832.
4. J. Alber, H. Fernau, and R. Niedermeier, Parameterized complexity: Exponential speed-up for planar graph problems, J Algorithms 52 (2004), 26-56.
5. N. Alon, P. Seymour, and R. Thomas, A separator theorem for nonplanar graphs, J Am Math Soc 3 (1990), 801-808.
6. N. Alon, P. Seymour, and R. Thomas, Planar separators, SIAM J Discrete Math 7 (1994), 184-193.
7. H. L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theor Comp Sci 209 (1998), 1-45.
8. J. F. Buss and J. Goldsmith, Nondeterminism within P, SIAM J Comput 22 (1993), 560-572.
9. J. Chen, I. A. Kanj, and W. Jia, Vertex cover: Further observations and further improvements, J Algorith 41 (2001), 280-301.
10. H. N. Djidjev and S. M. Venkatesan, Reduced constants for simple cycle graph separation, Acta Informatica 34 (1997), 231-243.
11. R. G. Downey and M. R. Fellows, Parameterized complexity, Springer-Verlag, New York, 1999.
12. 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.
13. F. V. Fomin and D. M. Thilikos, A simple and fast approach for solving problems on planar graphs, in Proceedings of the 21st International Symposium on Theoretical Aspects of Computer Science (STAGS 2004), Vol. 2996 of LNCS, Springer, Berlin, 2004, pp. 56-67.
14. 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 LNCS, Springer, Berlin, 2002, pp. 399-410.
15. R. J. Lipton and R. E. Tarjan, A separator theorem for planar graphs, SIAM J Appl Math 36 (1979), 177-189.
16. R. J. Lipton and R. E. Tarjan, Applications of a planar separator theorem, SIAM J Comput 9 (1980), 615-627.
17. G. L. Nemhauser and L. E. Trotter, Jr., Vertex packings: Structural properties and algorithms, Math Program 8 (1975), 232-248.
18. N. Robertson and P. D. Seymour, Graph minors. X. Obstructions to tree-decomposition, J Combin Theory Ser B 52 (1991), 153-190.
19. N. Robertson and P. D. Seymour, Graph minors. XI. Circuits on a surface, J Combin Theory Ser B 60 (1994), 72-106.
20. N. Robertson and P. D. Seymour, Graph minors. XI. Circuits on a surface, J Combin Theory Ser B 60 (1994), 72-106.
21. N. Robertson, P. D. Seymour, and R. Thomas, Quickly excluding a planar graph, J Combin Theory Ser B 62 (1994), 323-348.
22. P. D. Seymour and R. Thomas, Call routing and the ratcatcher, Combinatorica 14 (1994), 217-241.
23. R. Thomas, Tree-decompositions of graphs, http://www.math.gatech.edu/ ~thomas/SLIDE/slide2.ps, p. 32.