Abstract
The nearest neighbor interchange (nni) distance is a classical metric for measuring the distance (dissimilarity) between two evolutionary trees. The problem of computing the nni distance has been studied over two decades (see e.g., [16,3,7,12,8,4]). The long-standing conjecture that the problem is NP-complete was proved only recently, whereas approximation algorithms for the problem have appeared in the literature for a while. Existing approximation algorithms actually perform reasonably well (precisely, the approximation ratios are log n for unweighted trees and 4 log n for weighted trees); yet they are designed for degree-3 trees only. In this paper we present new approximation algorithms that can handle trees with non-uniform degrees. The running time is O(n 2) and the approximation ratios are respectively (\( \left( {\frac{{2d}} {{\log d}} + 2} \right) \)) log n and (\( \left( {\frac{{2d}} {{\log d}} + 12} \right) \)) log n for unweighted and weighted trees, where d ≥ 4 is the maximum degree of the input trees.
Research supported in part by Hong Kong RGC Grant HKU-7027/98E.
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© 1999 Springer-Verlag Berlin Heidelberg
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Hon, WK., Lam, TW. (1999). Approximating the Nearest Neighbor Interchange Distance for Evolutionary Trees with Non-uniform Degrees. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_6
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