Monotonicity Checking

  • M. Kyureghyan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


In our thesis we cosidered the complexity of the monotonicity checking problem: given a finite poset and an unknown real-valued function on it find out whether this function is monotone. Two decision models were considered: the comparison model, where the queries are usual comparisons, and the linear model, where the queries are comparisons of linear combinations of the input. This is a report on our results.


Comparison Model Hasse Diagram Boolean Lattice Cover Graph IEEE 16th Annual Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aigner, M.: Combinatorial Search. Wiley-Teubner Series in Computer Science, Stuttgart (1988)Google Scholar
  2. 2.
    Geissinger, L.: A polytope associated to a finite ordered set (preprint)Google Scholar
  3. 3.
    Goldreich, O., Goldwasser, S., Lehman, E., Ron, D., Samorodnitsky, A.: Testing monotonicity. Combinatorica, 301–337 (2000)Google Scholar
  4. 4.
    Kyureghyan, M.: Monotonicity checking, PhD Thesis, Universität Bielefeld, Bielefeld (2004)Google Scholar
  5. 5.
    Moravek, J., Pudlak, P.: New lower bound for the polyhedral membership problem with an application to linear programming. In: Chytil, M.P., Koubek, V. (eds.) MFCS 1984. LNCS, vol. 176, pp. 416–424. Springer, Berlin (1984)CrossRefGoogle Scholar
  6. 6.
    Stanley, R.: Two poset polytopes. Discrete Comput. Geom. 1, 9–23 (1986)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Voronenko, A.: On the complexity of recognizing monotonicity. Mathematical problems in cybernetics, No. 8 (Russian), Mat. Vopr. Kibern. 8, 301–303 (1999)Google Scholar
  8. 8.
    Yao, A., Rivest, R.: On the Polyhedral Decision Problem. SIAM J. Comput. 9, 343–347 (1980)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Yao, A.: On the complexity of comparison problems using linear decision trees. In: Proc. IEEE 16th Annual Symposium on foundations of Computer Science, pp. 85–89 (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. Kyureghyan

There are no affiliations available

Personalised recommendations