Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles IEEE/ACM Transactions on Computational Biology and Bioinformatics Year : 2009

Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

Abstract

Given a set $L$ of labels and a collection of rooted trees whose leaves are bijectively labelled by some elements of $L$, the Maximum Agreement Supertree problem (SMAST) is as follows: find a tree $T$ on a largest label set $L' \subseteq L$ that homeomorphically contains every input tree restricted to $L'$. The problem has phylogenetic applications to infer supertrees and perform tree congruence analyses. In this paper, we focus on the parameterized complexity of this NP-hard problem, considering different combinations of parameters as well as particular cases. We show that SMAST on $k$ rooted binary trees on a label set of size $n$ can be solved in $O((8n)^k)$ time, which is an improvement with respect to the previously known $O(n^{3k^2})$ time algorithm. In this case, we also give an $O((2k)^p kn^2)$ time algorithm, where $p$ is an upper bound on the number of leaves of $L$ missing in a SMAST solution. This shows that SMAST can be solved efficiently when the input trees are mostly congruent. Then for the particular case where any triple of leaves is contained in at least one input tree, we give $O(4^p n^3)$ and $O(3.12^p+n^4)$ time algorithms, obtaining the first fixed-parameter tractable algorithms on a single parameter for this problem. We also obtain intractability results for several combinations of parameters, thus indicating that it is unlikely that fixed-parameter tractable algorithms can be found in these particular cases.
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Dates and versions

lirmm-00324055 , version 1 (23-09-2008)

Identifiers

Cite

Sylvain Guillemot, Vincent Berry. Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2009, 7 (2), pp.342-353. ⟨10.1109/TCBB.2008.93⟩. ⟨lirmm-00324055⟩
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