Solving the Persistent Phylogeny Problem in polynomial time

The notion of a Persistent Phylogeny generalizes the well-known Perfect phylogeny model that has been thoroughly investigated and is used to explain a wide range of evolutionary phenomena. More precisely, while the Perfect Phylogeny model allows each character to be acquired once in the entire evolutionary history while character losses are not allowed, the Persistent Phylogeny model allows each character to be both acquired and lost exactly once in the evolutionary history. The Persistent Phylogeny Problem (PPP) is the problem of reconstructing a Persistent phylogeny tree, if it exists, from a binary matrix where the rows represent the species (or the individuals) studied and the columns represent the characters that each species can have. While the Perfect Phylogeny has a linear-time algorithm, the computational complexity of PPP has been posed, albeit in an equivalent formulation, 20 years ago. We settle the question by providing a polynomial time algorithm for the Persistent Phylogeny problem.