Inferring perfect phylogenies with restrictions on character state transitions

One of the important problems in evolutionary biology is inferring phylogenetic trees for sets of related species. We introduce a new model for inferring phylogenies which is a generalization of the widely studied perfect phylogeny model. The perfect phylogeny model assumes that a feature shared by a set of species cannot have evolved independently in any two of the species in the set, i.e. the species with this feature form a subtree in the correct phylogenetic tree. We briefly review earlier similar results on this subject and describe the difference between our model and the ones previously investigated. It turns out that the problem of finding a perfect phylogeny with restrictions is NP-complete even if the number of characters is 2. This contrasts with the complexity of finding unrestricted perfect phylogenies. On the other hand, the new model shows similar properties to the classical perfect phylogeny model in case where the number of cycles in each state transition graph is bounded by a small constant.