Abstract

Given n taxa, exactly one topology for every subset of four taxa, and a positive integer k (the parameter), the Minimum Quartet Inconsistency (MQI) problem is the question whether we can find an evolutionary tree inducing a set of quartet topologies that di#ers 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 fixedparameter intractable. For MQI, however, which is also NP-complete, we can compute the required tree in time O(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 e#ciently. In particular, for minimal k, our algorithm can produce all solutions that resolve k errors. Additionally, we discuss significant heuristic improvements.

Citations