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 [2] to n log n. Second, we present a counterexample disproving several theorems in [13]. Roughly speaking, finding an equal partition between two trees doesn't 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.
Supported in part by the NSERC Operating Grant OGP0046506, ITRC, a CGAT grant and DIMACS.
Supported by an NSERC International Fellowship.
Supported by a CGAT grant.
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© 1996 Springer-Verlag Berlin Heidelberg
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Li, M., Tromp, J., Zhang, L. (1996). Some notes on the nearest neighbour interchange distance. In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_168
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DOI: https://doi.org/10.1007/3-540-61332-3_168
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