# A Faster Construction of Greedy Consensus Trees

## TL;DR

This paper presents significantly faster algorithms for constructing greedy and frequency difference consensus trees, reducing computational complexity from quadratic to near-linear time in key parameters, thereby improving phylogenetic analysis efficiency.

## Contribution

The paper introduces improved algorithms that reduce the running time for computing greedy and frequency difference consensus trees from quadratic to near-linear time complexities.

## Key findings

- Greedy consensus tree algorithm improved to  O(k n^{1.5})
- Frequency difference consensus tree algorithm improved to  O(k n)
- Significant reduction in computational complexity for phylogenetic consensus methods

## Abstract

A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications in predicting a species tree from a set of gene trees. This paper focuses on two of the most well-known and widely used oconsensus tree methods: the greedy consensus tree and the frequency difference consensus tree. Given $k$ conflicting trees each with $n$ leaves, the previous fastest algorithms for these problems were $O(k n^2)$ for the greedy consensus tree [J. ACM 2016] and $\tilde O(\min \{ k n^2, k^2n\})$ for the frequency difference consensus tree [ACM TCBB 2016]. We improve these running times to $\tilde O(k n^{1.5})$ and $\tilde O(k n)$ respectively.