This problem is a pattern matching problem on leaf-labeled trees. Each input tree is considered as a branching pattern inducing specific groups of leaves. Given a tree collection with identical leaf sets, the goal is to find a largest subset of leaves on the branching pattern of which the input trees do not disagree. A maximum compatible tree is a tree with such a leaf-set and with the branching patterns of the input trees for these leaves. The Maximum Compatible Tree problem (MCT) is to find such a tree or, equivalently, its leaf set. The main motivation for this problem is in phylogenetics, to measure the similarity between evoluti ...