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A consensus tree is a single phylogenetic tree that summarizes the branching structure in a given set of conflicting phylogenetic trees. Many different types of consensus trees have been proposed in the literature; three of the most well-known and widely used ones are the majority rule consensus tree, the loose consensus tree, and the greedy consensus tree. This article presents new deterministic algorithms for constructing them that are faster than all the previously known ones. Given k phylogenetic trees with n leaves each and with identical leaf label sets, our algorithms run in O(nk) time (majority rule consensus tree), O(nk) time (loose consensus tree), and O(n2k) time (greedy consensus tree). Our algorithms for the majority rule consensus and the loose consensus trees are optimal since the input size is Ω(nk). Experimental results show that the algorithms are fast in practice.

Improved Algorithms for Constructing Consensus Trees