Computing a Consensus Phylogeny via Leaf Removal

Abstract

Given a set $\mathcal{T} = \{T_1, T_2, \ldots , T_m\}$ of phylogenetic trees with the same leaf-label set X, we wish to remove some leaves from the trees so that there is a tree T with leaf-label set X displaying all the resulting trees. One objective is to minimize the total number of leaves removed from the trees, while the other is to minimize the maximum number of leaves removed from an input tree. Chauve et al. [6] refer to the problem with the first (respectively, second) objective as AST-LR (respectively, AST-LR-d), and show that both problems are NP-hard. They further present algorithms for the parameterized versions of both problems, but it seems that their algorithm for the parameterized version of AST-LR is flawed [7]. In this paper, we present a new algorithm for the parameterized version of AST-LR and also show that Chauve et al.’s algorithm for the parameterized version of AST-LR-d can be sped up by an exponential factor. We further design heuristic integer-linear programming (ILP for short) models for AST-LR and AST-LR-d. Our experimental results show that the heuristic models can be used to significantly speed up solving the exact models proposed in [7].