A Probabilistic Approach to Problems Parameterized above or below Tight Bounds

  • Gregory Gutin
  • Eun Jung Kim
  • Stefan Szeider
  • Anders Yeo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5917)


We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds or below tight upper bounds. To illustrate the approach we consider two problems of this type of unknown complexity that were introduced by Mahajan, Raman and Sikdar (J. Comput. Syst. Sci. 75, 2009). We show that a generalization of one of the problems and three nontrivial special cases of the other problem admit kernels of quadratic size.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N.: Voting paradoxes and digraphs realizations. Advances in Applied Math. 29, 126–135 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Alon, N., Gutin, G., Krivelevich, M.: Algorithms with large domination ratio. J. Algorithms 50(1), 118–131 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, London (2009)zbMATHGoogle Scholar
  4. 4.
    Blyth, T.S., Robertson, E.F.: Basic Linear Algebra. Springer, Heidelberg (2000)Google Scholar
  5. 5.
    Bourgain, J.: Walsh subspaces of \(L\sp{p}\)-product spaces. In: Seminar on Functional Analysis (1979–1980) (French)Google Scholar
  6. 6.
    Coppersmith, D.: Solving linear systems over GF(2): block Lanczos algorithm. Lin. Algebra Applic. 192, 33–60 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  8. 8.
    Flum, J., Grohe, M.: arameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series, vol. XIV. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    Gutin, G., Kim, E.J., Mnich, M., Yeo, A.: Ordinal Embedding Relaxations Parameterized Above Tight Lower Bound. Tech. Report arXiv:0907.5427Google Scholar
  10. 10.
    Gutin, G., Rafiey, A., Szeider, S., Yeo, A.: The linear arrangement problem parameterized above guaranteed value. Theory Comput. Syst. 41, 521–538 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gutin, G., Szeider, S., Yeo, A.: Fixed-parameter complexity of minimum profile problems. Algorithmica 52(2), 133–152 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Håstad, J., Venkatesh, S.: On the advantage over a random assignment. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, vol. 25(2), pp. 117–149 (2002)Google Scholar
  13. 13.
    Heggernes, P., Paul, C., Telle, J.A., Villanger, Y.: Interval completion with few edges. In: STOC 2007—Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 374–381. ACM, New York (2007); Full version appeared in SIAM J. Comput. 38(5) (2008-2009)Google Scholar
  14. 14.
    Mahajan, M., Raman, V.: Parameterizing above guaranteed values: MaxSat and MaxCut. J. Algorithms 31(2), 335–354 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Mahajan, M., Raman, V., Sikdar, S.: Parameterizing above or below guaranteed values. J. of Computer and System Sciences 75(2), 137–153 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2006)CrossRefzbMATHGoogle Scholar
  17. 17.
    Vovk, V.: Private communication (August 2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gregory Gutin
    • 1
  • Eun Jung Kim
    • 1
  • Stefan Szeider
    • 2
  • Anders Yeo
    • 1
  1. 1.Department of Computer ScienceRoyal Holloway, University of LondonEgham, SurreyUK
  2. 2.Department of Computer ScienceDurham UniversityDurham, EnglandUK

Personalised recommendations