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.
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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)
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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
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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
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