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Walks on SPR Neighborhoods
Jan.-Feb. 2013 (vol. 10 no. 1)
pp. 236-239
Alan Joseph J. Caceres, Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA
Juan Castillo, Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA
Jinnie Lee, Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA
Katherine St. John, Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA
A nearest-neighbor-interchange (NNI)-walk is a sequence of unrooted phylogenetic trees, T1,T2, ... ,Tk 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.
Index Terms:
trees (mathematics),biology computing,evolution (biological),genetics,sequences,Bryant second combinatorial challenge,nearest-neighbor-interchange walk,unrooted phylogenetic trees sequence,consecutive trees pair,subtree-prune-and-regraft neighborhood,unrooted binary tree,Nearest neighbor searches,Decision trees,graphs and networks,Analysis of algorithms and problem complexity,biology and genetics,trees
Citation:
Alan Joseph J. Caceres, Juan Castillo, Jinnie Lee, Katherine St. John, "Walks on SPR Neighborhoods," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 1, pp. 236-239, Jan.-Feb. 2013, doi:10.1109/TCBB.2012.136
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