Algorithms for the Majority Rule (+) Consensus Tree and the Frequency Difference Consensus Tree

TL;DR

This paper introduces two efficient deterministic algorithms for constructing consensus trees from multiple phylogenetic trees, optimizing for time complexity and handling large datasets effectively.

Contribution

It presents the first optimal algorithm for the majority rule (+) consensus tree and a new efficient algorithm for the frequency difference consensus tree.

Findings

Majority rule (+) consensus tree constructed in optimal O(kn) time.

Frequency difference consensus tree constructed in min(O(kn^2), O(kn (k+log^2 n))) time.

Algorithms are deterministic and suitable for large phylogenetic datasets.

Abstract

This paper presents two new deterministic algorithms for constructing consensus trees. Given an input of k phylogenetic trees with identical leaf label sets and n leaves each, the first algorithm constructs the majority rule (+) consensus tree in O(kn) time, which is optimal since the input size is Omega(kn), and the second one constructs the frequency difference consensus tree in min(O(kn^2), O(kn (k+log^2 n))) time.