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Hamiltonian Walks of Phylogenetic Treespaces
July-Aug. 2013 (vol. 10 no. 4)
pp. 1076-1079
Kevaughn Gordon, Dept. of Math. & Comput. Sci., City Univ. of New York, New York, NY, USA
Eric Ford, Dept. of 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
We answer Bryant's combinatorial challenge on minimal walks of phylogenetic treespace under the nearest-neighbor interchange (NNI) metric. We show that the shortest path through the NNI-treespace of n-leaf trees is Hamiltonian for all n. That is, there is a minimal path that visits all binary trees exactly once, under NNI moves.
Index Terms:
trees (mathematics),bioinformatics,evolution (biological),genetics,genomics,Hamiltonian walks,binary trees,n-leaf trees,NNI-treespace,nearest-neighbor interchange metric,phylogenetic treespaces,Measurement,Binary trees,Phylogeny,Silicon,Computational biology,Bioinformatics,Computer science,analysis of algorithms,Phylogenetic tree construction,graph theory
Citation:
Kevaughn Gordon, Eric Ford, Katherine St. John, "Hamiltonian Walks of Phylogenetic Treespaces," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 10, no. 4, pp. 1076-1079, July-Aug. 2013, doi:10.1109/TCBB.2013.105
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