A sub-cubic time algorithm for computing the quartet distance between two general trees

Background: When inferring phylogenetic trees different algorithms may give different trees. To study such effects a measure for the distance between two trees is useful. Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees. Results: We have derived a new algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree >= 3. The time and space complexity of our algorithm is sub-cubic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm so far for computing the quartet distance between general trees independent of the degree of the inner nodes. Conclusions: We have implemented our algorithm and two of the best competitors. Our new algorithm is significantly faster than the competition and seems to run in close to quadratic time in practice.