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Parameterized and approximation algorithms for maximum agreement forest in multifurcating trees. (English) Zbl 1303.68154
Summary: 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 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 $$O(3^k n)$$-time parameterized algorithm for 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 general trees.

##### MSC:
 68W25 Approximation algorithms 92D15 Problems related to evolution
rSPR
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##### References:
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