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A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem

Author

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  • Catanzaro, Daniele

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

  • Frohn, Martin
  • Gascuel, Olivier
  • Pesenti, Raffaele

Abstract

We build upon recent theoretical advances on the Balanced Minimum Evolution Problem (BMEP) to design a new massively parallel exact solution algorithm that proves to be up to one order of magnitude faster than the current state-of-the-art under the same computing settings and environment. We also investigate, for the first time, the theoretical connections between numerical stability and statistical consistency of the BMEP and we show that some rescaling techniques introduced to numerically stabilize the problem may affect negatively the statistical consistency of the optimal solution to the problem.

Suggested Citation

  • Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2023. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2023001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2023001
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    References listed on IDEAS

    as
    1. Catanzaro, Daniele & Aringhieri, Roberto & Di Summa, Marco & Pesenti, Raffaele, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 753-765.
    2. 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.
    3. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    4. 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).
    5. Daniele Catanzaro & Raffaele Pesenti, 2019. "Enumerating vertices of the balanced minimum evolution polytope," LIDAM Reprints CORE 3005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. Daniele CATANZARO & Roberto ARINGHIERI & Mardo DI SUMMA & Raffaele PESENTI, 2015. "A branch-price-and-cut algorithm for the minimum evolution problem," LIDAM Reprints CORE 2767, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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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