Abstract
We study parameterized algorithms and approximation algorithms for the maximum agreement forest problem, which, for two given leaf-labeled trees, is to find a maximum forest that is a subgraph of both trees. The problem was motivated by the research in phylogenetics. For parameterized algorithms, while the problem is known to be fixed-parameter tractable for binary trees, it was an open problem whether the problem is still fixed-parameter tractable for general trees. We resolve this open problem by developing an O(3k n)-time parameterized algorithm for the problem on general trees. Our techniques on tree structures also lead to a polynomial-time approximation algorithm of ratio 3 for the problem, giving the first constant-ratio approximation algorithm for the problem on general trees.
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Chen, J., Fan, JH., Sze, SH. (2013). Parameterized and Approximation Algorithms for the MAF Problem in Multifurcating Trees. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 2013. Lecture Notes in Computer Science, vol 8165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45043-3_14
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DOI: https://doi.org/10.1007/978-3-642-45043-3_14
Publisher Name: Springer, Berlin, Heidelberg
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