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Median Approximations for Genomes Modeled as Matrices.

Joao Paulo Pereira Zanetti¹, Priscila Biller², Joao Meidanis^2,3

¹Institute of Computing, University of Campinas, Campinas, Brazil. jppzanetti@gmail.com.

Bulletin of Mathematical Biology

|April 14, 2016

Summary

This study introduces new methods for the genome median problem, finding a fourth genome that best fits three given genomes. The approach models genomes as matrices and offers improved median candidates for phylogenetic reconstruction.

Keywords:

Approximated algorithms Genome median problem Phylogenetic reconstruction Subspace decomposition

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Area of Science:

Computational Biology
Bioinformatics
Phylogenetic Reconstruction

Background:

The genome median problem is crucial for understanding evolutionary relationships between species.
Existing methods for finding genome medians have limitations in approximation accuracy.

Purpose of the Study:

To develop novel algorithms for the genome median problem using matrix representations.
To identify new median candidates with improved approximation ratios.

Main Methods:

Modeling genomes as matrices and applying rank distance.
Developing an approximation algorithm to compute additional median candidates.
Proposing a heuristic to convert matrix solutions back to genomes.

Main Results:

Identified up to three new matrix median candidates with approximation ratios as good as or better than existing methods.
Demonstrated optimality for a specific class of instances.
Validated the heuristic's effectiveness in converting matrix solutions to genomes.

Conclusions:

The proposed methods offer potentially more useful genome median candidates, located farther from trivial solutions.
The approach shows promise for accurate phylogenetic reconstruction, as evidenced by simulated evolution tests and comparison with exact solvers.