Abstract
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.
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References
Alon, N.: Voting paradoxes and digraphs realizations. Advances in Applied Math. 29, 126–135 (2002)
Alon, N., Gutin, G., Krivelevich, M.: Algorithms with large domination ratio. J. Algorithms 50(1), 118–131 (2004)
Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, London (2009)
Blyth, T.S., Robertson, E.F.: Basic Linear Algebra. Springer, Heidelberg (2000)
Bourgain, J.: Walsh subspaces of \(L\sp{p}\)-product spaces. In: Seminar on Functional Analysis (1979–1980) (French)
Coppersmith, D.: Solving linear systems over GF(2): block Lanczos algorithm. Lin. Algebra Applic. 192, 33–60 (1993)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Flum, J., Grohe, M.: arameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series, vol. XIV. Springer, Heidelberg (2006)
Gutin, G., Kim, E.J., Mnich, M., Yeo, A.: Ordinal Embedding Relaxations Parameterized Above Tight Lower Bound. Tech. Report arXiv:0907.5427
Gutin, G., Rafiey, A., Szeider, S., Yeo, A.: The linear arrangement problem parameterized above guaranteed value. Theory Comput. Syst. 41, 521–538 (2007)
Gutin, G., Szeider, S., Yeo, A.: Fixed-parameter complexity of minimum profile problems. Algorithmica 52(2), 133–152 (2008)
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)
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)
Mahajan, M., Raman, V.: Parameterizing above guaranteed values: MaxSat and MaxCut. J. Algorithms 31(2), 335–354 (1999)
Mahajan, M., Raman, V., Sikdar, S.: Parameterizing above or below guaranteed values. J. of Computer and System Sciences 75(2), 137–153 (2009)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2006)
Vovk, V.: Private communication (August 2009)
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Gutin, G., Kim, E.J., Szeider, S., Yeo, A. (2009). A Probabilistic Approach to Problems Parameterized above or below Tight Bounds. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_19
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DOI: https://doi.org/10.1007/978-3-642-11269-0_19
Publisher Name: Springer, Berlin, Heidelberg
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