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On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

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.

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Correspondence to Magnus Bordewich.

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Received March 16, 2004

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Bordewich, M., Semple, C. On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance. Ann. Comb. 8, 409–423 (2005). https://doi.org/10.1007/s00026-004-0229-z

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AMS Subject Classification.

  • 05C05
  • 92D15

Keywords.

  • rooted phylogenetic tree
  • rooted subtree prune and regraft