A linear kernel for planar feedback vertex set

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

Volumn 5018 LNCS, Issue , 2008, Pages 160-171

  Bodlaender, Hans L ^a   Penninkx, Eelko ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; POLYNOMIALS; PROBLEM SOLVING;

FEEDBACK VERTEX SET; KERNELIZATION ALGORITHM; SUBGRAPHS;

SET THEORY;

EID: 44649163366     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-79723-4_16     Document Type: Conference Paper

References (35)

1. Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial-time data reduction for dominating sets. J. ACM 51, 363-384 (2004)
2. Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Disc. Math. 12, 289-297 (1999)
3. Bar-Yehuda, R., Geiger, D., Naor, J., Roth, R.M.: Approximation algorithms for the vertex feedback set problem with applications to constraint satisfaction and Bayesian inference. In: Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1994, pp. 344-354 (1994)
4. Becker, A., Bar-Yehuda, R., Geiger, D.: Randomized algorithms for the loop cutset problem. J. Artificial Intelligence Research 12, 219-234 (2000)
5. Becker, A., Geiger, D.: Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem. Artificial Intelligence 83, 167-188 (1996)
6. Bodlaender, H.L.: On disjoint cycles. Int. J. Found. Computer Science 5(1), 59-68 (1994)
7. Bodlaender, H.L.: A cubic kernel for feedback vertex set. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 320-331. Springer, Heidelberg (2007)
8. Burrage, K., Estivill-Castro, V., Fellows, M.R., Langston, M.A., Mac, S., Rosamond, F.A.: The undirected feedback vertex set problem has a poly(k) kernel. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 192-202. Springer, Heidelberg (2006)
9. Chen, J., Fomin, F.V., Liu, Y., Lu, S., Villanger, Y.: Improved algorithms for the feedback vertex set problems. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 422-433. Springer, Heidelberg (2007)
10. Chen, J., Liu, Y., Lu, S., O'Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem. In: Proceedings STOC 2008 (to appear, 2008)
11. Chudak, F., Goemans, M., Hochbaum, D., Williamson, D.: A primal-dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Operations Research Letters 22, 111-118 (1998)
12. 3) FPT algorithm for the undirected feedback vertex set problem. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 859-869. Springer, Heidelberg (2005)
13. Demaine, E.D., Hajiaghayi, M.: Bidimensionality: New connections between FPT algorithms and PTASs. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 590-601 (2005)
14. Dorn, F.: Dynamic programming and fast matrix multiplication. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 280-291. Springer, Heidelberg (2006)
15. Dorn, F., Penninkx, E., Bodlaender, H.L., Fomin, F.V.: Efficient exact algorithms on planar graphs: Exploiting sphere cut branch decompositions. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 95-106. Springer, Heidelberg (2005)
16. Downey, R.G., Fellows, M.R.: Fixed-parameter tractability and completeness. Congressus Numerantium 87, 161-178 (1992)
17. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)
18. Festa, P., Pardalos, P.M., Resende, M.G.C.: Feedback set problems. In: Handbook of Combinatorial Optimization, Amsterdam, The Netherlands, vol. A, pp. 209-258. Kluwer, Dordrecht (1999)
19. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
20. n). In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 183-191. Springer, Heidelberg (2006)
21. Fomin, F.V., Thilikos, D.M.: New upper bounds on the decomposability of planar graphs. J. Graph Theory 51, 53-81 (2006)
22. Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)
23. Goemans, M.X., Williamson, D.P.: Primal-dual approximation algorithms for feedback problems in planar graphs. Combinatorica 17, 1-23 (1997)
24. Guo, J., Gramm, J., Hffner, F., Niedermeier, R., Wernicke, S.: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. Journal of Computer and System Sciences 72(8), 1386-1396 (2006)
25. Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News 38, 31-45 (2007)
26. Hackbusch, W.: On the feedback vertex set problem for a planar graph. Computing 58, 129-155 (1997)
27. Kanj, I.A., Pelsmajer, M.J., Schaefer, M.: Parameterized algorithms for feedback vertex set. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 235-248. Springer, Heidelberg (2004)
28. Kloks, T., Lee, C.M., Liu, J.: New algorithms for k-face cover, k-feedback vertex set, and k-disjoint cycles on plane and planar graphs. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 282-295. Springer, Heidelberg (2002)
29. Mehlhorn, K., Näher, S.: LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1995)
30. Niedermeier, R.: Invitation to fixed-parameter algorithms. Universität Tübingen, Habilitation Thesis (2002)
31. Raman, V., Saurabh, S., Subramanian, C.R.: Faster fixed parameter tractable algorithms for undirected feedback vertex set. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 241-248. Springer, Heidelberg (2002)
32. Raman, V., Saurabh, S., Subramanian, C.R.: Faster algorithms for feedback vertex set. In: Proceedings 2nd Brazilian Symposium on Graphs, Algorithms, and Combinatorics, GRACO 2005. Electronic Notes in Discrete Mathematics, vol. 19, pp. 273-279 (2005)
33. Razgon, I.: Exact computation of maximum induced forest. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 160-171. Springer, Heidelberg (2006)
34. Stamm, H.: On feedback problems in planar digraphs. In: Möhring, R.H. (ed.) WG 1990. LNCS, vol. 484, pp. 79-89. Springer, Heidelberg (1991)
35. van Dijk, T.: Fixed parameter complexity of feedback problems. Master's thesis, Utrecht University (2007)