Facets of the Balanced Minimal Evolution Polytope
Stefan Forcey, Logan Keefe, William Sands
TL;DR
This paper explores the geometric structure of the BME polytope, which is used in constructing phylogenetic trees via the balanced minimal evolution method, by initiating the study of its facets.
Contribution
It provides the first steps towards describing the facets of the BME polytope, linking phylogenetics and polyhedral combinatorics.
Findings
Initiated the study of BME polytope facets.
Connected phylogenetic tree optimization with polyhedral geometry.
Lays groundwork for future polytope characterization.
Abstract
A phylogenetic tree is a way to organize a finite set of species, individuals or other sources of related data. The species for which we have existing DNA data make up the set of leaves of the tree. The balanced minimal evolution method of creating phylogenetic trees can be formulated as a linear programming problem, minimizing an inner product over the vertices of the BME polytope. In this paper we undertake the first steps of describing the facets of this polytope.
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Taxonomy
TopicsGenomics and Phylogenetic Studies · Genome Rearrangement Algorithms · Genetic diversity and population structure