On the nearest neighbour interchange distance between evolutionary trees

Journal of Theoretical Biology
M LiL Zhang

Abstract

We present some new results on a well-known distance measure between evolutionary trees. The trees we consider are free 3-trees having n leaves labeled 0,...,n - 1 (representing species), and n - 2 internal nodes of degree 3. The distance between two trees is the minimum number of nearest neighbour interchange (NNI) operations required to transform one into the other. First, we improve an upper bound on the nni-distance between two arbitrary n-node trees from 4n log n (Culik & Wood, 1982, Inf. Pro. Letts. 15, 39-42) to n log n. Second, we present a counterexample disproving several theorems in (Waterman & Smith, 1978, J. theor. Biol. 73, 789-800). Roughly speaking, finding an equal partition between two trees does not imply decomposability of the distance finding problem. Third, we present a polynomial-time approximation algorithm that, given two trees, finds a transformation between them of length O(log n) times their distance. We also present some results of computations we performed on small size trees.

Citations

Feb 14, 2006·BMC Evolutionary Biology·Robert G Beiko, Nicholas Hamilton
Dec 21, 2011·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Yu LinBernard M E Moret
Mar 9, 2011·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Damian Bogdanowicz, Krzysztof Giaro
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Feb 18, 2016·IEEE/ACM Transactions on Computational Biology and Bioinformatics·Pawel Pawel GoreckiOliver Eulenstein
Sep 19, 2017·International Journal of Systematic and Evolutionary Microbiology·In-Tae ChaMyung-Ji Seo
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Jun 12, 2021·Algorithms for Molecular Biology : AMB·Katharina JahnLouxin Zhang
Jul 5, 2021·Environmental Science and Pollution Research International·Khomdram Niren Singh, Diganta Narzary

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