Abstract
Given two unrooted, binary trees, T1 and T2, leaf labelled bijectively by a set of species L, the Maximum Agreement Forest (MAF) problem asks to find a minimum cardinality collection F = {t1, ..., tk} of phylogenetic trees where each element of F is a subtree of both T1 and T2, the elements of F are pairwise disjoint, and the leaf labels for the elements of F partition the leaf label set L. We give an efficient fixed-parameter tractable (FPT) algorithm for the MAF problem, significantly improving on an FPT algorithm given in [2]. Whereas the algorithm from [2] has a running time of O(k3k) + p(|L|), our algorithm runs in time O(4k · k5) + p(|L|), where k bounds the size of the agreement forest and p(·) is a low order polynomial.
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Hallett, M., McCartin, C. A Faster FPT Algorithm for the Maximum Agreement Forest Problem. Theory Comput Syst 41, 539–550 (2007). https://doi.org/10.1007/s00224-007-1329-z
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DOI: https://doi.org/10.1007/s00224-007-1329-z