Walks on SPR Neighborhoods

Author

Caceres, Alan Joseph J. ; Castillo, Javier ; Lee, Jeyull ; St.John, K.

Author_Institution

Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA

Volume

10

Issue

1

fYear

2013

fDate

Jan.-Feb. 2013

Firstpage

236

Lastpage

239

Abstract

A nearest-neighbor-interchange (NNI)-walk is a sequence of unrooted phylogenetic trees, T₁,T₂, ... ,T_k where each consecutive pair of trees differs by a single NNI move. We give tight bounds on the length of the shortest NNI-walks that visit all trees in a subtree-prune-and-regraft (SPR) neighborhood of a given tree. For any unrooted, binary tree, T, on n leaves, the shortest walk takes ⊖(n²) additional steps more than the number of trees in the SPR neighborhood. This answers Bryant´s Second Combinatorial Challenge from the Phylogenetics Challenges List, the Isaac Newton Institute, 2011, and the Penny Ante Problem List, 2009.

Keywords

biology computing; evolution (biological); genetics; sequences; trees (mathematics); Bryant second combinatorial challenge; consecutive trees pair; nearest-neighbor-interchange walk; subtree-prune-and-regraft neighborhood; unrooted binary tree; unrooted phylogenetic trees sequence; Decision trees; Nearest neighbor searches; Analysis of algorithms and problem complexity; biology and genetics; graphs and networks; trees; Algorithms; Computational Biology; Evolution, Molecular; Models, Genetic; Phylogeny;

fLanguage

English

Journal_Title

Computational Biology and Bioinformatics, IEEE/ACM Transactions on

Publisher

ieee

ISSN

1545-5963

Type

jour

DOI

10.1109/TCBB.2012.136

Filename

6342945