The strict clustering algorithm performs poorly, but the relaxed clustering algorithm performs almost as well as the greedy algorithm. All analyses were conducted on a phylogenomic dataset of birds (Table 1, Hackett_2008). Note that lower scores indicate a better fit of the model to the data. The dashed line in each plot shows the score of the best partitioning scheme found by the greedy algorithm. Each boxplot represent the distribution of scores for 1000 runs of the strict or relaxed clustering algorithms, where each run uses a different definition of the similarity of two subsets (see main text). The figure shows that the relaxed clustering algorithm’s performance approaches that of the greedy algorithm as P increases, and that analysing 10% of partitioning schemes results in information theoretic scores that are very close to that of the greedy algorithm.