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New heuristics for phylogeny estimation under the balanced minimum evolution criterion.

Daniele Catanzaro1, Henri Dehaybe1, Raffaele Pesenti2

  • 1Center for Operations Research and Econometrics, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium.

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New algorithms improve the Balanced Minimum Evolution Problem (BMEP) by leveraging mathematical insights and computational frameworks. These enhanced methods offer superior solutions for reconstructing evolutionary trees.

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Area of Science:

  • Phylogenetics
  • Computational Biology
  • Discrete Mathematics

Background:

  • Recent advances in combinatorics have characterized matrices for Unrooted Binary Tree Path-Length Matrices.
  • This led to an integer linear programming formulation for the Balanced Minimum Evolution Problem (BMEP).
  • This formulation is the current reference exact solution algorithm.

Purpose of the Study:

  • To improve approximation algorithms for the BMEP using recent mathematical advances.
  • To develop enhanced heuristics based on the BMEP's linear programming relaxation.
  • To further enhance solution quality using a Beam Search framework.

Main Methods:

  • Leveraging the tight linear programming relaxation of the BMEP formulation.
  • Developing an enhanced Neighbor Joining-like heuristic.
  • Embedding the heuristic within a Beam Search framework.

Main Results:

  • The proposed algorithms outperform existing heuristics for the BMEP.
  • Computational experiments demonstrate the effectiveness of the enhanced methods.
  • The developed algorithms provide higher quality solutions for evolutionary tree reconstruction.

Conclusions:

  • The study successfully improved BMEP approximation algorithms.
  • The enhanced heuristic and Beam Search framework offer practical advantages.
  • These methods are highly desirable for accurate evolutionary tree inference.