Bidimensionality and kernels

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2010, Pages 503-510

  Fomin, Fedor V ^a   Lokshtanov, Daniel ^a   Saurabh, Saket ^b   Thilikos, Dimitrios M ^c  

^a UNIVERSITY OF BERGEN   (Norway)

^b INSTITUTE OF MATHEMATICAL SCIENCES   (India)

^c UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHIC METHODS; PARAMETERIZATION; POLYNOMIAL APPROXIMATION;

ALGORITHMIC TECHNIQUES; BIDIMENSIONALITY THEORY; CONNECTED DOMINATING SET; EXPONENTIAL TIME ALGORITHM; PARAMETERIZED ALGORITHM; PARAMETERIZED COMPLEXITY; POLYNOMIAL TIME APPROXIMATION SCHEMES; POLYNOMIAL-TIME ALGORITHMS;

PARAMETER ESTIMATION;

EID: 77951687684     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973075.43     Document Type: Conference Paper

References (32)

1. M. AKRA AND L. BAZZI, On the solution of linear recurrence equations, Computational Optimization and Applications, 10 (1998), pp. 195-210.
2. 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.
3. J. ALBER, M. R. FELLOWS, AND R. NIEDERMEIER, Polynomial-time data reduction for dominating sets, J. ACM, 51 (2004), pp. 363-384.
4. N. ALON AND S. GUTNER, Kernels for the dominating set problem on graphs with an excluded minor, Tech. Rep. TR08-066, Electronic Colloquium on Computational Complexity (ECCC), 2008.
5. H. BODLAENDER, F. V. FOMIN, D. LOKSHTANOV, E. PENNINKX, S. SAURABH, AND D. M. THILIKOS, (Meta) kernelization, in FOCS'09, IEEE Comput. Soc. Press, 2009, p. to appear.
6. H. L. BODLAENDER, A partial k-arboretum of graphs with bounded treewidth, Theor. Comp. Sc., 209 (1998), pp. 1-45.
7. H. L. BODLAENDER, R. G. DOWNEY, M. R. FELLOWS, AND D. HERMELIN, On problems without polynomial kernels, in Proc. 35th ICALP, vol. 5125 of LNCS, Springer, 2008, pp. 563-574.
8. H. L. BODLAENDER AND E. PENNINKX, A linear kernel for planar feedback vertex set, in Proceedings Third International Workshop on Parameterized and Exact Computation, IWPEC 2008, M. Grohe and R. Niedermeier, eds., Springer Verlag, Lecture Notes in Computer Science, vol. 5018, 2008, pp. 160-171.
9. H. L. BODLAENDER, E. PENNINKX, AND R. B. TAN, A linear kernel for the k-disjoint cycle problem on planar graphs, in Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC), vol. 5369 of LNCS, Springer, 2008, pp. 306-317.
10. H. L. BODLAENDER AND B. VAN ANTWERPENDE FLUITER, Reduction algorithms for graphs of small treewidth, Information and Computation, 167 (2001), pp. 86-119.
11. J. CHEN, H. FERNAU, I. A. KANJ, AND G. XIA, Parametric duality and kernelization: Lower bounds and upper bounds on kernel size, in Proc. 22nd STACS, vol. 3404 of LNCS, Springer, 2005, pp. 269-280.
12. -, Parametric duality and kernelization: Lower bounds and upper bounds on kernel size, SIAM J. Comput., 37 (2007), pp. 1077-1106.
13. J. CHEN, I. A. KANJ, AND W. JIA, Vertex Cover: Further observations and further improvements, J. Algorithms, 41 (2001), pp. 280-301.
14. B. DE FLUITER, Algorithms for Graphs of Small Treewidth, PhD thesis, Utrecht University, 1997.
15. E. DEMAINE AND M. HAJIAGHAYI, The bidimensionality theory and its algorithmic applications, The computer Journal, (2007), pp. 332-337.
16. E. D. DEMAINE, F. V. FOMIN, M. HAJIAGHAYI, AND D. M. THILIKOS, Bidimensional parameters and local treewidth, SIAM J. Discrete Math., 18 (2004/2005), pp. 501-511.
17. E. D. DEMAINE, F. V. FOMIN, M. HAJIAGHAYI, AND D. M. THILIKOS, Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs, J. ACM, 52 (2005), pp. 866-893.
18. E. D. DEMAINE AND M. HAJIAGHAYI, Bidimensionality: New connections between FPT algorithms and PTASs, in Proc. 16th SODA, ACM/SIAM, 2005, pp. 590-601.
19. E. D. DEMAINE AND M. HAJIAGHAYI, Linearity of grid minors in treewidth with applications through bidimensionality, Combinatorica, 28 (2008), pp. 19-36.
20. F. DORN, F. V. FOMIN, AND D. M. THILIKOS, Subexponential parameterized algorithms, Comp, Sc. Rev., 2 (2008), pp. 29-39.
21. R. G. DOWNEY AND M. R. FELLOWS, Parameterized Complexity, Springer, 1999.
22. J. FLUM AND M. GROHE, Parameterized Complexity Theory, Texts in Theoretical Computer Science. An EATCS Series, Springer-Verlag, Berlin, 2006.
23. F. V. FOMIN, P. A. GOLOVACH, AND D. M. THILIKOS, Contraction bidimensionality: the accurate picture, in ESA'09, LNCS, 2009, p. to appear.
24. J. GUO AND R. NIEDERMEIER, Invitation to data reduction and problem kernelization, SIGACT News, 38 (2007), pp. 31-45.
25. -, Linear problem kernels for NP-hard problems on planar graphs, in Proc. 34th ICALP, vol. 4596 of LNCS, Springer, 2007, pp. 375-386.
26. J. GUO, R. NIEDERMEIER, AND S. WERNICKE, Fixed-parameter tractability results for full-degree spanning tree and its dual, in Proceedings of the Second International Workshop on Parameterized and Exact Computation (IWPEC), vol. 4169 of LNCS, Springer, 2006, pp. 203-214.
27. I. A. KANJ, M. J. PELSMAJER, G. XIA, AND M. SCHAEFER, On the induced matching problem, in Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2008), vol. 08001, Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, Berlin, 2008, pp. 397-408.
28. D. LOKSHTANOV, M. MNICH, AND SAURABH, Linear kernel for planar connected dominating set, in Proceedings of Theory and Applications of Models of Computation, (TAMC 2009), Lecture Notes in Comput. Sci., Springer, 2009.
29. H. MOSER AND S. SIKDAR, The parameterized complexity of the induced matching problem in planar graphs, in Proceedings First Annual International WorkshopFrontiers in Algorithmics (FAW), vol. 4613 of LNCS, Springer, 2007, pp. 325-336.
30. R. NIEDERMEIER, Invitation to fixed-parameter algorithms, vol. 31 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2006.
31. i,j-free and d-degenerate graphs, manuscript, 2009.
32. S. THOMASSÉ, A quadratic kernel for feedback vertex set, in Proc. 20th SODA, ACM/SIAM, 2009, pp. 115-119.