On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance
نویسنده
چکیده
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.
منابع مشابه
A 3-approximation algorithm for the subtree distance between phylogenies
In this paper, we give a (polynomial-time) 3-approximation algorithm for the rooted subtree prune and regraft distance between two phylogenetic trees. This problem is known to be NP-complete and the best previously known approximation algorithm is a 5-approximation. We also give a faster fixed-parameter algorithm for the rooted subtree prune and regraft distance than was previously known.
متن کاملA practical method for exact computation of subtree prune and regraft distance
MOTIVATION Subtree prune and regraft (SPR) is one kind of tree rearrangements that has seen applications in solving several computational biology problems. The minimum number of rooted SPR ((r)SPR) operations needed to transform one rooted binary tree to another is called the (r)SPR distance between the two trees. Computing the (r)SPR distance has been actively studied in recent years. Currentl...
متن کاملApproximating Subtree Distances Between Phylogenies
We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cas...
متن کاملA Unifying View on Approximation and FPT of Agreement Forests
We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linearor O(n logn)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridizat...
متن کاملA Unifying View on Approximation and FPT of Agreement Forests (Extended Abstract⋆)
We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linearor O(n log n)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridiza...
متن کامل