On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
On distances between phylogenetic trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Maximum Agreement Forest on k trees
Information Processing Letters
A unifying view on approximation and FPT of agreement forests
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Fast FPT algorithms for computing rooted agreement forests: theory and experiments
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
A practical approximation algorithm for solving massive instances of hybridization number
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
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There are various techniques for reconstructing phylogenetic trees from data, and in this context the problem of determining how distant two such trees are from each other arises naturally. Various metrics for measuring the distance between two phylogenies have been defined. Another way of comparing two trees T and U is to compute the so called maximum agreement forest of these trees. Informally, the number of components of an agreement forest tells how many edges from each of T and U need to be cut so that the resulting forests agree, after performing all forced edge contractions. This problem is NP-hard even when the input trees have maximum degree 2. Hein et al. [J. Hein, T. Jiang, L. Wang, K. Zhang, On the complexity of comparing evolutionary trees, Discrete Applied Mathematics 71 (1996) 153-169] presented an approximation algorithm for it, claimed to have performance ratio 3. We show that the performance ratio of the algorithm proposed by Hein et al. is 4, and we also present two new 3-approximation algorithms for this problem. We show how to modify one of the algorithms into a (d+1)-approximation algorithm for trees with bounded degree d, d=2. Finally, we report on some computational experiments comparing the performance of the algorithms presented in this paper.