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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

    (Universit`a Ca’ Foscari di Venezia)

  • Pisanu, Francesco

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

Abstract

The Balanced Minimum Evolution Problem (BMEP) is an APX -hard nonlinear network design problem that has received attention from the bioinformatics and mathematical programming communities over the past two decades. In this work, we show that if all input distances are positive and bounded, this problem admits a polynomial-time approximation algorithm. We also identify some polynomially solvable instances of the BMEP, including additive dissimilarity matrices, and derive tight lower and upper bounds on the optimal solution to the problem.

Suggested Citation

  • Catanzaro, Daniele & Pesenti, Raffaele & Pisanu, Francesco, 2025. "A Note on the Approximability of the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2025021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2025021
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    References listed on IDEAS

    as
    1. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2022. "A tutorial on the balanced minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 1-19.
    2. Catanzaro, Daniele & Pesenti, Raffaele & Wolsey, Laurence, 2020. "On the balanced minimum evolution polytope," LIDAM Reprints CORE 3096, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Catanzaro, Daniele & Pesenti, Raffaele & Sapucaia, Allan & Wolsey, Laurence, 2025. "Optimizing over Path-Length Matrices of Unrooted Binary Trees," LIDAM Reprints CORE 3321, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Daniele Catanzaro & Martine Labbé & Raffaele Pesenti & Juan-José Salazar-González, 2012. "The Balanced Minimum Evolution Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 276-294, May.
    5. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2020. "An information theory perspective on the balanced minimum evolution problem," LIDAM Reprints CORE 3097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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