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On the Neighborhoods of Trees
May-June 2013 (vol. 10 no. 3)
pp. 721-728
Peter J. Humphries, Dept. of Math. & Phys., North Carolina Central Univ., Durham, NC, USA
Taoyang Wu, Sch. of Comput. Sci., Univ. of East Anglia, Norwich, UK
Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighborhood, that is, the number of trees exactly one operation from a given tree. We present an exact expression for the size of the TBR (tree bisection and reconnection) neighborhood, thus answering a question first posed by Allen and Steel . In addition, we also obtain a characterization of the extremal trees whose TBR neighborhoods are maximized and minimized.
Index Terms:
trees (mathematics),biology computing,evolution (biological),genetics,TBR neighborhood minimization,tree neighborhood size,tree rearrangement operation,phylogenetic tree space metric,tree number,TBR neighborhood size expression,tree bisection and reconnection neighborhood,extremal tree characterization,TBR neighborhood maximization,Vegetation,Phylogeny,Binary trees,Measurement,Indexes,Shape,Steel,unit neighborhood,trees (mathematics),biology computing,evolution (biological),genetics,TBR neighborhood minimization,tree neighborhood size,tree rearrangement operation,phylogenetic tree space metric,tree number,TBR neighborhood size expression,tree bisection and reconnection neighborhood,extremal tree characterization,TBR neighborhood maximization,Vegetation,Phylogeny,Binary trees,Measurement,Indexes,Shape,Steel,phylogenetics,Tree rearrangement,tree bisection and reconnection
Citation:
Peter J. Humphries, Taoyang Wu, "On the Neighborhoods of Trees," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 3, pp. 721-728, May-June 2013, doi:10.1109/TCBB.2013.66
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