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Facets of the balanced minimal evolution polytope
Stefan Forcey1, Logan Keefe2, William Sands2
1Department of Mathematics, The University of Akron, Akron, OH, 44325-4002, USA. sf34@uakron.edu.
Journal of Mathematical Biology
|December 31, 2015
Summary
Researchers describe the facets of the balanced minimal evolution (BME) polytope, a key step in creating phylogenetic trees. This work advances understanding of BME polytope geometry for efficient tree-finding algorithms.
Area of Science:
- Computational Biology
- Phylogenetics
- Discrete Geometry
Background:
- The balanced minimal evolution (BME) method is a key algorithm for constructing phylogenetic trees.
- Phylogenetic tree construction can be framed as a linear programming problem involving the BME polytope.
- Understanding the geometry of the BME polytope is crucial for optimizing this method.
Purpose of the Study:
- To describe the facets of the BME polytope.
- To classify the combinatorial structure and geometry of BME polytope facets.
- To lay the groundwork for efficient relaxations of the BME polytope.
Main Methods:
- Formulating the BME method as a linear programming problem.
- Analyzing the vertices of the BME polytope.
- Classifying facet inequalities in dimensions up to five and beyond.
Main Results:
- Identification and classification of BME polytope facets in dimensions up to five.
- Characterization of the combinatorial structure and geometric properties (facet inequalities) of these facets.
- A broader classification of additional facets across all dimensions.
Conclusions:
- The detailed description of BME polytope facets provides essential insights into the BME method.
- These findings represent a significant step towards developing efficient relaxations of the BME polytope.
- While a full simplex method implementation remains challenging, this research paves the way for practical algorithmic improvements.
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