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On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances

Bordewich, Magnus; Scornavacca, Celine; Tokac, Nihan; Weller, Mathias

On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances Thumbnail


Celine Scornavacca

Nihan Tokac

Mathias Weller


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.


Bordewich, M., Scornavacca, C., Tokac, N., & Weller, M. (2017). On the Fixed Parameter Tractability of Agreement-based Phylogenetic Distances. Journal of Mathematical Biology, 74(1), 239-257.

Journal Article Type Article
Acceptance Date May 9, 2016
Online Publication Date May 25, 2016
Publication Date Jan 1, 2017
Deposit Date May 12, 2016
Publicly Available Date May 25, 2017
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 74
Issue 1
Pages 239-257


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