A simple and fast approach for solving problems on planar graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2996, Issue , 2004, Pages 56-67

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

^a UNIVERSITY OF BERGEN   (Norway)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DYNAMIC PROGRAMMING; GRAPHIC METHODS; PROBLEM SOLVING; TREES (MATHEMATICS);

ALGORITHM DESIGN; BRANCH DECOMPOSITION; COMPLEXITY RESULTS; DIVIDE AND CONQUER; GRAPH ALGORITHMS; INDEPENDENT SET; SEPARATION THEOREM; SIMPLE APPROACH;

GRAPH THEORY;

EID: 35048828350     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24749-4_6     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, M. R. FELLOWS, AND R. NIEDERMEIER, Efficient data reduction for dominating set: A linear problem kernel for the planar case, in SWAT 2002, Springer, vol. 2368, Berlin, 2002, pp. 150-159.
3. J. ALBER, H. FERNAU, AND R. NIEDERMEIER, Parameterized complexity: Exponential speed-up for planar graph problems, in Electronic Colloquium on Computational Complexity (ECCC), Germany, 2001.
4. J. ALBER, II. FERNAU, AND R. NIEDERMEIER, Graph separators: a parameterized view, J. of Computer and System Sciences, (2003), to appear.
5. N. ALON, P. SEYMOUR, AND R. THOMAS, A separator theorem for nonplanar graphs, J. Amer. Math. Soc., 3 (1990), pp. 801-808.
6. -, Planar separators, SIAM J. Discrete Math., 7 (1994), pp. 184-193.
7. H. L. BODLAENDER, On linear time minor tests with depth-first search, J. Algorithms, 14 (1993), pp. 1-23.
8. M.-S. CHANG, T. KLOKS, AND C.-M. LEE, Maximum clique transversals, in WG 2001, vol. 2204 of Lecture Notes in Comput. Sci., Springer, Berlin, 2001, pp. 32-43.
9. J. CHEN, I. A. KANJ, AND W. JIA, Vertex cover: further observations and further improvements, J. Algorithms, 41 (2001), pp. 280-301.
10. n algorithm for k-SAT based on local search, Theoret. Comput. Sci., 289 (2002), pp. 69-83.
11. E. D. DEMAINE, F. V. FOMIN, M. HAJIAGHAYI, AND D. M. THILIKOS, Fixedparameter algorithms for the (k, r) -center in planar graphs and map graphs, in ICALP 2003, vol. 2719 of Lecture Notes in Comput. Sci., Springer, Berlin, 2003, pp. 829-844.
12. 5-minor-free graphs, in ISAAC 2002, Springer, Lecture Notes in Computer Science, Berlin, vol. 2518, 2002, pp. 262-273.
13. J. DIAZ, M. SERNA, AND D. M. THILIKOS, Counting H-colorings of partial k-trees, Theoretical Computer Science, 281 (2002), pp. 291-309.
14. H. N. DJIDJEV AND S. M. VENKATESAN, Reduced constants for simple cycle graph separation, Acta Informatica, 34 (1997), pp. 231-243.
15. R. G. DOWNEY AND M. R. FELLOWS, Parameterized complexity, Springer-Verlag, New York, 1999.
16. D. EPPSTEIN, Small maximal independent sets and faster exact graph coloring, in WADS 2001, vol. 2125 of Lecture Notes in Comput. Sei., Springer, Berlin, 2001, pp. 462-470.
17. U. FEIGE, Coping with the NP-hardness of the graph bandwidth problem, in SWAT 2000. vol. 1851 of Lecture Notes in Comput. Sci., Springer, Berlin, 2000, pp. 10-19.
18. F. V. FOMIN AND D. M. THILIKOS, Dominating sets in planar graphs: Branchwidth and exponential speed-up, in SODA 2003, pp. 168-177.
19. G. GUTIN, T. KLOKS, AND C. M. LEE, Kernels in planar digraphs, in Optimization Online, Mathematical Programming Society, Philadelphia, 2001.
20. M. M. HALLDÓRSSON AND G. KORTSARZ, Tools for multicoloring with applications to planar graphs and partial k-trees, Journal of Algorithms, 42 (2002), pp. 334-366.
21. I. V. HICKS, Branch Decompositions and their applications, PhD thesis, Rice University, 2000.
22. K. JANSEN, M. KARPINSKI, A. LINGAS, AND E. SEIDEL, Polynomial time approximation schemes for Max-Bisection on planar and geometric graphs, in STAGS 2001. vol. 2010 of Lecture Notes in Comput. Sci., Springer, Berlin, 2001, pp. 365-375.
23. I. KANJ AND L. PERKOVIĆ, Improved parameterized algorithms for planar dominating set, in MFCS 2002, Springer, Lecture Notes in Computer Science, Berlin, vol. 2420, 2002, pp. 399-410.
24. R. J. LIPTON AND R. E. TARJAN, A separator theorem for planar graphs, SIAM J. Appl. Math., 36 (1979), pp. 177-189.
25. -, Applications of a planar separator theorem, SIAM J. Comput., 9 (1980), pp. 615-627.
26. N. ROBERTSON AND P. D. SEYMOUR, Graph minors. X. Obstructions to treedecomposition, J. Combin. Theory Ser. B, 52 (1991), pp. 153-190.
27. -, Graph minors. XI. Circuits on a surface, J. Combin. Theory Ser. B, 60 (1994), pp. 72-106.
28. N. ROBERTSON, P. D. SEYMOUR, AND R. THOMAS, Quickly excluding a planar graph, J. Combin. Theory Ser. B, 62 (1994), pp. 323-348.
29. P. D. SEYMOUR AND R. THOMAS, Call routing and the ratcatcher, Combinatorica, 14 (1994), pp. 217-241.
30. J. A. TELLE AND A. PROSKUROWSKI, Algorithms for vertex partitioning problems on partial k-trees, SIAM J. Discrete Math., 10 (1997), pp. 529-550.
31. G. J. WOEGINGER, Exact algorithms for NP-hard problems: a survey, in Combinatorial Optimization-Eureka, You Shrink!, M. Junger, G. Reinelt, and G. Rinaldi, eds., Springer, LNCS 2570, Berlin, 2003, pp. 185-207.