A Fixed-Parameter Enumeration Algorithm for the Weighted FVS Problem

  • Jianxin Wang
  • Guohong Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


In this paper, we present a fixed-parameter enumeration algorithm for the feedback vertex set problem by using the branch-and-search method. The algorithm transforms the feedback vertex set problem to the feedback edge set problem with specific conditions. Then it enumerates the z minimum-weight feedback edge sets by enumerating the z maximum-weight forests. As a result, we show the problem of enumerating the z minimum-weight feedback vertex sets of size k is solvable in time \(\mathcal {O}(5^{k}kn^{2}+(5^{k}+3^{k}z)n^{2}\log n)\).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Becker, A., Bar-Yehuda, R., Geiger, D.: Randomized algorithms for the loop cutset problem. J. Artif. Intell. Res. (JAIR) 12, 219–234 (2000)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Bodlaender, H.L.: On disjoint cycles. In: Proceedings of the 17th International Workshop, pp. 230–238. Springer, London (1992)Google Scholar
  3. 3.
    Chen, J., Fomin, F., 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)CrossRefGoogle Scholar
  4. 4.
    Chen, J., Kanj, I., Meng, J., Xia, G., Zhang, F.: On the effective enumerability of NP problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 215–226. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Dehne, F., Fellows, M., Langston, M., Rosamond, F., Stevens, K.: An O(2o(k) n 3) FPT algorithm for the undirected feedback vertex set problem. Theory Comput. Syst. 41(3), 479–492 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Downey, R., Fellows, M.: Fixed parameter tractability and completeness. In: Complexity Theory: Current Research, pp. 191–225. Cambridge University, Cambridge (1992)Google Scholar
  7. 7.
    Downey, R., Fellows, M.: Parameterized complexity. Springer, New York (1999)Google Scholar
  8. 8.
    Guo, J., Gramm, J., Hüffner, F., Niedermeier, R., Wernicke, S.: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. J. Comput. Syst. Sci. 72(8), 1386–1396 (2006)zbMATHCrossRefGoogle Scholar
  9. 9.
    Kanj, I., Pelsmajer, M., Schaefer, M.: Parameterized algorithms for feedback vertex set. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 235–247. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Raman, V., Saurabh, S., Subramanian, C.: 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)CrossRefGoogle Scholar
  11. 11.
    Raman, V., Saurabh, S., Subramanian, C.: Faster fixed parameter tractable algorithms for finding feedback vertex sets. ACM Transactions on Algorithms 2(3), 403–415 (2006)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Sörensen, K., Janssens, G.: An algorithm to generate all spanning trees of a graph in order of increasing cost. Pesquisa Operacional 25(2), 219–229 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jianxin Wang
    • 1
  • Guohong Jiang
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina

Personalised recommendations