# The asymmetric median tree — A new model for building consensus trees

## Abstract

Inferring the consensus of a set of different evolutionary trees for a given species set is a well-studied problem, for which several different models have been proposed. In this paper, we propose a new optimization problem for consensus tree construction, which we call the *asymmetric median tree*, or *AMT*. Our main theoretical result is the equivalence between the asymmetric median tree problem on *k* trees and the maximum independent set (MIS) problem on *k*-colored graphs. Although the problem is *NP-hard* for three or more trees, we have polynomial time algorithms to construct the AMT for two trees and an approximation algorithm for three or more trees. We define a measure of phylogenetic resolution and show that our algorithms (both exact and approximate) produce consensus trees that on every input are at least as resolved as the standard models (strict consensus and majority tree) in use. Finally, we show that the AMT combines desirable features of many of the standard consensus tree models in use.

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