title: Walks on SPR neighborhoods.
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 Θ(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.
authors.affiliation: Department of Mathematics and Computer Science, Lehman College-City University of New York, 250 Bedford Park Boulevard West, Bronx, NY 10468, USA. alan.j.caceres@gmail.com
authors.forename: Alan Joseph J
authors.initials: AJ
authors.lastname: Caceres
authors.forename: Juan
authors.initials: J
authors.lastname: Castillo
authors.forename: Jinnie
authors.initials: J
authors.lastname: Lee
authors.forename: Katherine
authors.initials: K
authors.lastname: St John
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D019143:Evolution, Molecular; D008957:Models, Genetic; D010802:Phylogeny