A short note on the tractability of constructing phylogenetic networks from clusters

TL;DR

This paper presents a polynomial-time algorithm for constructing level-k phylogenetic networks from clusters, extending previous results and suggesting the potential for efficient algorithms in this area.

Contribution

It introduces a theoretical polynomial-time algorithm for all levels k, broadening the scope beyond level 2 networks.

Findings

Polynomial-time algorithm for level-k networks for all k

Strengthens the possibility of fixed parameter tractable algorithms

Supports the feasibility of efficient phylogenetic network construction

Abstract

In [2] it was proven that the Cass algorithm is a polynomial-time algorithm for constructing level<=2 networks from clusters. Here we demonstrate, for each k>=0, a polynomial-time algorithm for constructing level-k phylogenetic networks from clusters. Unlike Cass the algorithm scheme given here is only of theoretical interest. It does, however, strengthen the hope that efficient polynomial-time algorithms (and perhaps fixed parameter tractable algorithms) exist for this problem.