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A note on the approximability of the balanced minimum evolution problem

Author

Listed:
  • Catanzaro, Daniele

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Pesenti, Raffaele

    (Università Ca’ Foscari di Venezia)

  • Pisanu, Francesco

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

The Balanced Minimum Evolution Problem (BMEP) is a highly nonlinear -hard optimization problem in molecular phylogenetics that has attracted significant attention from the bioinformatics and mathematical programming communities. We investigate conditions under which its practical instances become efficiently approximable. We show that when all pairwise distances are positive and bounded, the problem admits a polynomial-time approximation algorithm with a performance guarantee linked to the interval width. We also characterize polynomially solvable instances, and derive tight bounds on the optimal solution.

Suggested Citation

  • Catanzaro, Daniele & Pesenti, Raffaele & Pisanu, Francesco, 2026. "A note on the approximability of the balanced minimum evolution problem," LIDAM Reprints CORE 3353, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3353
    DOI: https://doi.org/10.1016/j.orl.2026.107438
    Note: In: Operations Research Letters, 2026, vol. 67, 107438
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