'Bureaucratic' set systems, and their role in phylogenetics

TL;DR

This paper characterizes bureaucratic set systems, explores their role in phylogenetics, and presents a polynomial-time algorithm for a related parsimony problem in phylogenetic networks.

Contribution

It introduces the concept of bureaucratic set systems, characterizes them, and applies this framework to develop efficient algorithms in phylogenetics.

Findings

Characterization of bureaucratic set systems

Application to phylogenetics frameworks

Polynomial-time algorithm for a phylogenetic parsimony problem

Abstract

We say that a collection $\Cc$ of subsets of $X$ is {\em bureaucratic} if every maximal hierarchy on $X$ contained in $\Cc$ is also maximum. We characterise bureaucratic set systems and show how they arise in phylogenetics. This framework has several useful algorithmic consequences: we generalize some earlier results and derive a polynomial-time algorithm for a parsimony problem arising in phylogenetic networks.