Abstract
Given two finite posets P and Q, P is a chain minor of Q if there exists a partial function f from the elements of Q to the elements of P such that for every chain in P there is a chain C Q in Q with the property that f restricted to C Q is an isomorphism of chains.
We give an algorithm to decide whether a poset P is a chain minor of a poset Q that runs in time \(\mathcal{O}(|Q| log |Q|)\) for every fixed poset P. This solves an open problem from the monograph by Downey and Fellows [Parameterized Complexity, 1999] who asked whether the problem was fixed parameter tractable.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Yuster, R., Zwick, U.: Color-coding. Journal of the ACM 42(4), 844–856 (1995)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, NewYork (1999)
Fomin, F.V., Marx, D.: FPT suspects and tough customers: Open problems of Downey and Fellows (submitted)
Gustedt, J.: Algorithmic Aspects of Ordered Structures. PhD thesis, Berlin (1992)
Gustedt, J.: Well Quasi Ordering Finite Posets and Formal Languages. Journal of Combinatorial Theory, Series B 65(1), 111–124 (1995)
Möhring, R.H., Müller, R.: A combinatorial approach to obtain bounds for stochastic project networks. Tech. report, Technische Universität Berlin (1992)
Naor, M., Schulman, L.J., Srinivasan, A.: Splitters and near-optimal derandomization. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science FOCS (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Błasiok, J., Kamiński, M. (2013). Chain Minors Are FPT. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-03898-8_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03897-1
Online ISBN: 978-3-319-03898-8
eBook Packages: Computer ScienceComputer Science (R0)