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On the fixed parameter tractability of agreement-based phylogenetic distances.

Bordewich, Magnus and Scornavacca, Celine and Tokac, Nihan and Weller, Mathias (2017) 'On the fixed parameter tractability of agreement-based phylogenetic distances.', Journal of mathematical biology., 74 (1). pp. 239-257.

Abstract

Three important and related measures for summarizing the dissimilarity in phylogenetic trees are the minimum number of hybridization events required to fit two phylogenetic trees onto a single phylogenetic network (the hybridization number), the (rooted) subtree prune and regraft distance (the rSPR distance) and the tree bisection and reconnection distance (the TBR distance) between two phylogenetic trees. The respective problems of computing these measures are known to be NP-hard, but also fixed-parameter tractable in their respective natural parameters. This means that, while they are hard to compute in general, for cases in which a parameter (here the hybridization number and rSPR/TBR distance, respectively) is small, the problem can be solved efficiently even for large input trees. Here, we present new analyses showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any O(f(p)⋅n)O(f(p)⋅n)-time algorithm for any of these problems into an O(f(k)⋅n)O(f(k)⋅n)-time one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic network displaying both trees.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00285-016-1023-3
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-016-1023-3
Date accepted:09 May 2016
Date deposited:23 May 2016
Date of first online publication:25 May 2016
Date first made open access:25 May 2017

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