A quadratic kernel for computing the hybridization number of multiple trees

It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel.

► We study computing the hybridization number of sets of rooted phylogenetic trees. ► We show fixed-parameter tractability for arbitrarily many binary trees. ► In particular, there exists a quadratic kernel. ► To establish this result, we use two reductions and the concept of generators. ► Previously, only heuristics were known for this problem.