Greedy Consensus Tree and Maximum Greedy Consensus Tree Problems

Abstract

Consensus tree is a phylogenetic tree that summarizes the branching information of a set of conflicting phylogenetic trees. Computing consensus tree is a major step in phylogenetic tree reconstruction. It also finds application in predicting a species tree from a set of gene trees. Here, we focus our study on one of the most frequently used consensus tree problem, called greedy consensus tree problem. Given k phylogenetic trees leaf-labeled by n taxa, previous best known algorithm for constructing a greedy consensus tree of these k trees runs in $O(k n^{1.5} \log n)$ time. Here, we describe an $O(k^2 n)$-time solution. Our method is the fastest when $k = O(\sqrt{n} \log n)$.

Existing greedy consensus tree methods may not report the most resolved greedy consensus tree. Here, we propose a new computational problem called the maximum greedy consensus tree problem that aims to find the most resolved greedy consensus tree. We showed that this problem is NP-hard for $k \ge 3$. We also give a polynomial time solution when $k=2$ and an approximation algorithm for $k=3$.