Abstract
Given two rooted binary phylogenetic trees with identical leaf label-set, the maximum agreement forest (MAF) problem asks for a largest common subforest of the two trees. This problem has been studied extensively in the literature, and has been known to be NP-complete and MAX SNP-hard. The previously best ratio of approximation algorithms for this problem is 3. In this paper, we make full use of the special relations among leaves in phylogenetic trees and present an approximation algorithm with ratio 2.5 for the MAF problem on two rooted binary phylogenetic trees.
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Notes
The definitions for the study of MAFs have been kind of confusing. If size denotes the number of edges in a forest, then for a forest, the size is equal to the number of vertices minus the order. In particular, when the number of vertices is fixed, a forest of a large size means a small order of the forest.
Allen and Steel (2001) proved that the TBR distance between two unrooted binary phylogenetic trees is equal to the order of their MAF minus 1.
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Acknowledgments
A preliminary version of this work was reported in the Proceedings of the 8th International Frontiers of Algorithmics Workshop, Lecture Notes in Computer Science, vol. 8497, pp. 205–215, 2014. This work is supported by the National Natural Science Foundation of China under Grant (61232001, 61472449, 61420106009), the Major Science & Technology Research Program for Strategic Emerging Industry of Hunan (Grant No. 2012GK4054), and the Research Fund for the Doctoral Program of Higher Education of China (No. 20130162130001).
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Shi, F., Feng, Q., You, J. et al. Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees. J Comb Optim 32, 111–143 (2016). https://doi.org/10.1007/s10878-015-9921-7
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DOI: https://doi.org/10.1007/s10878-015-9921-7