Finding a maximum compatible tree is NP-hard for sequences and trees Original Research Article

We show that the following two related problems arising in phylogenetic analysis are NP-hard: 1. (i) given a collection of aligned 2-state sequences, find the largest subset of sequences compatible with some tree, 2. (ii) given six trees, leaf-labelled by S, find the largest subset S′ of S so that the six subtrees induced by S′ are compatible.