Near-Optimal Algorithm for Constructing Greedy Consensus Tree

Abstract

In biology, phylogenetic trees are important tools for describing evolutionary relations, but various data sources may result in conflicting phylogenetic trees. To summarize these conflicting phylogenetic trees, consensus tree methods take k conflicting phylogenetic trees (each with n leaves) as input and output a single phylogenetic tree as consensus. Among the consensus tree methods, a widely used method is the greedy consensus tree. The previous fastest algorithms for constructing a greedy consensus tree have time complexity O(kn^1.5) [Gawrychowski, Landau, Sung, Weimann 2018] and O(k²n) [Sung 2019] respectively. In this paper, we improve the running time to O(kn). Since k input trees have Θ(kn) nodes in total, our algorithm is optimal up to polylogarithmic factors.