A fixed-parameter algorithm for minimum quartet inconsistency

Given n taxa, exactly one topology for every subset of four taxa, and a positive integer k (the parameter), the M inimum Q uartet I nconsistency (MQI) problem is the question whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in only k quart...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 67; no. 4; pp. 723 - 741
Main Authors: Gramm, Jens, Niedermeier, Rolf
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2003
Subjects:
Computational biology
Minimum quartet inconsistency
Parameterized complexity
Phylogeny
Quartet methods
Quartet methods
Minimum quartet inconsistency
Phylogeny
Parameterized complexity
Computational biology
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:Given n taxa, exactly one topology for every subset of four taxa, and a positive integer k (the parameter), the M inimum Q uartet I nconsistency (MQI) problem is the question whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in only k quartet topologies. The more general problem where we are not necessarily given a topology for every subset of four taxa appears to be fixed-parameter intractable. For MQI, however, which is also NP-complete, we can compute the required tree in time O(4 k n+ n 4). This means that the problem is fixed-parameter tractable and that in the case of a small number k of “errors” the tree reconstruction can be done efficiently. In particular, for minimal k, our algorithm can produce all solutions that resolve k errors. Additionally, we discuss significant heuristic improvements. Experiments underline the practical relevance of our solutions.
ISSN:0022-0000
1090-2724
DOI:10.1016/S0022-0000(03)00077-1