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On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance
Magnus Bordewich1,2 and Charles Semple2
1School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom
magnusb@comp.leeds.ac.uk
2Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
c.semple@math.canterbury.ac.nz
Annals of Combinatorics 8 (4) p.409-423 December, 2006
AMS Subject Classification: 05C05, 92D15
Abstract:
The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.
Keywords: rooted phylogenetic tree, rooted subtree prune and regraft

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