Algorithms for Computing the Quartet Distance

Evolutionary (Phylogenetic) trees are constructs of the biological and medical sciences, their purpose is to establish the relationship between a set of species (phyla). Often it is the case that the true evolutionary tree is unknown and one can only try to estimate it. Reconstruction methods are manifold and the resulting evolutionary trees are not guaranteed to be correct. In order to establish the quality of constructed evolutionary trees one might consider a similarity measure on such trees. The quartet metric is one such possible measure. Quartets are trees containing precisely four species. A quartet has one of four possible topologies. The quartet distance between two trees is the number of quartets, containing the same four species, having different topologies. We have developed a framework for comparing evolutionary trees according to the quartet metric. Three applications of this framework have been analysed in this thesis. We have considered trees of arbitrary degree, trees of constant degree and finally considered calculating the pairwise quartet distance between multiple trees. Each of these applications have led to algorithms superior to existing algorithms with respect to both time and space.