General techniques for comparing unrooted evolutionary trees
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Tree Contractions and Evolutionary Trees
SIAM Journal on Computing
An O(n log n) algorithm for the maximum agreement subtree problem for binary trees
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
On distances between phylogenetic trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal evolutionary tree comparison by sparse dynamic programming
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
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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(n2) and the approximation ratios are respectively (2d/log d+2) log n and (2d/log d+12) log n for unweighted and weighted trees, where d ≥ 4 is the maximum degree of the input trees.