Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem ⋆

Abstract. Given a ground set L of labels and a collection of trees whose leaves are bijectively labelled by some elements of L, the Maximum Agreement Supertree problem (SMAST) is the following: find a tree T on a largest label set L ′ ⊆ L that homeomorphically contains every input tree restricted to L ′. The problem finds applications in phylogenetics, databases and data mining. In this paper we focus on the parameterized complexity of this NP-hard problem. We consider different combinations of parameters for SMAST as well as particular cases, providing both FPT algorithms and intractability results.