Fast error-tolerant quartet phylogeny algorithms

TL;DR

This paper introduces a fast, error-tolerant algorithm for phylogenetic reconstruction using quartets, achieving high accuracy and efficiency with probabilistic guarantees, outperforming existing heuristics.

Contribution

The authors develop an $O(n \, log \, n)$ time algorithm for quartet-based phylogeny that is both fast and consistent under a probabilistic model, with a novel balanced search tree approach.

Findings

Runs in $O(n \, log \, n)$ time with high probability

Provides consistency guarantees under a probabilistic model

Comparable runtime to the fastest heuristics in experiments

Abstract

We present an algorithm for phylogenetic reconstruction using quartets that returns the correct topology for $n$ taxa in $O(n \log n)$ time with high probability, in a probabilistic model where a quartet is not consistent with the true topology of the tree with constant probability, independent of other quartets. Our incremental algorithm relies upon a search tree structure for the phylogeny that is balanced, with high probability, no matter what the true topology is. Our experimental results show that our method is comparable in runtime to the fastest heuristics, while still offering consistency guarantees.