Parameterized and approximation algorithms for maximum agreement forest in multifurcating trees

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...

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Bibliographic Details
Published in:Theoretical computer science Vol. 562; pp. 496 - 512
Main Authors: Chen, Jianer, Fan, Jia-Hao, Sze, Sing-Hoi
Format: Journal Article
Language:English
Published: Elsevier B.V 2015
Subjects:
Algorithms
Approximation
Approximation algorithm
Fixed-parameter tractability
Forests
Mathematical analysis
Maximum agreement forest
Phylogenetic tree
Trees
Maximum agreement forest
Approximation algorithm
Fixed-parameter tractability
Phylogenetic tree
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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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(3kn)-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.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2014.10.031