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.

Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (TBR), subtree prune and regraft (SPR) and rooted subtree prune and regraft (rSPR). For a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is n−Θ( √ n), extending a result of Ding, ...

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...

Aim: To evaluate the efficacy of oral cyclosporin A in the prevention and treatment of immune graft rejection in heavily vascularised, repeated keratoplasties with high risk for failure. Methods: 21 consecutive patients with 28 repeated corneal transplants and four quadrant vascularised recipient bed were treated with oral cyclosporin A for an average period of 12 months (range 1–41 months) and...

AIM To evaluate the efficacy of oral cyclosporin A in the prevention and treatment of immune graft rejection in heavily vascularised, repeated keratoplasties with high risk for failure. METHODS 21 consecutive patients with 28 repeated corneal transplants and four quadrant vascularised recipient bed were treated with oral cyclosporin A for an average period of 12 months (range 1-41 months) and...

Aims: To determine the indications for penetrating keratoplasty (PK) at the Corneoplastic Unit and Eye Bank, UK, a tertiary referral centre, over a 10 year period. Methods: Records of all patients who underwent PK at our institution between 1990 and 1999 were reviewed retrospectively. Of the 1096 procedures performed in this period, 784 records were available for evaluation (72%). Results: Regr...

AIMS To determine the indications for penetrating keratoplasty (PK) at the Corneoplastic Unit and Eye Bank, UK, a tertiary referral centre, over a 10 year period. METHODS Records of all patients who underwent PK at our institution between 1990 and 1999 were reviewed retrospectively. Of the 1096 procedures performed in this period, 784 records were available for evaluation (72%). RESULTS Reg...

We prove that the spaces of unrooted phylogenetic trees are Hamiltonian for two popular search metrics: Subtree Prune and Regraft (SPR) and Tree Bisection and Reconnection (TBR). Further, we make progress on two conjectures of Bryant on searching phylogenetic treespace: treespace under the Nearest Neighbor Interchange (NNI) metric has a 2-walk, and there exists SPR neighborhoods without complet...

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...