Tropical medians by transportation

TL;DR

This paper explores Fermat-Weber points under asymmetric tropical distances, linking them to transportation problems, and introduces a novel method for computing consensus trees in phylogenetics with advantageous properties.

Contribution

It establishes a connection between tropical Fermat-Weber points and transportation problems, and proposes a new consensus tree method with Pareto properties.

Findings

Fermat-Weber points correspond to transportation problem solutions.

New method for phylogenetic consensus trees with Pareto properties.

Method improves on existing approaches in certain criteria.

Abstract

Fermat-Weber points with respect to an asymmetric tropical distance function are studied. It turns out that they correspond to the optimal solutions of a transportation problem. The results are applied to obtain a new method for computing consensus trees in phylogenetics. This method has several desirable properties; e.g., it is Pareto and co-Pareto on rooted triplets.