Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aigner, M.: Combinatorial Search. Wiley-Teubner Series in Computer Science, Stuttgart (1988)
Geissinger, L.: A polytope associated to a finite ordered set (preprint)
Goldreich, O., Goldwasser, S., Lehman, E., Ron, D., Samorodnitsky, A.: Testing monotonicity. Combinatorica, 301–337 (2000)
Kyureghyan, M.: Monotonicity checking, PhD Thesis, Universität Bielefeld, Bielefeld (2004)
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)
Stanley, R.: Two poset polytopes. Discrete Comput. Geom. 1, 9–23 (1986)
Voronenko, A.: On the complexity of recognizing monotonicity. Mathematical problems in cybernetics, No. 8 (Russian), Mat. Vopr. Kibern. 8, 301–303 (1999)
Yao, A., Rivest, R.: On the Polyhedral Decision Problem. SIAM J. Comput. 9, 343–347 (1980)
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)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kyureghyan, M. (2006). Monotonicity Checking. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_47
Download citation
DOI: https://doi.org/10.1007/11889342_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46244-6
Online ISBN: 978-3-540-46245-3
eBook Packages: Computer ScienceComputer Science (R0)