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On the approximability of the Fixed-Tree Balanced Minimum Evolution Problem

Author

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  • Frohn, Martin

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

Abstract

The Fixed-Tree BMEP (FT-BMEP) is a special case of the Balanced Minimum Evolution Problem (BMEP) that consists of finding the assignment of a set of n taxa to the n leaves of a given unrooted binary tree so as to minimize the BMEP objective function. Deciding the computational complexity of the FT-BMEP has been an open problem for almost a decade. Here, we show that a few modifications to Fiorini and Joret’s proof of the NP-hardness of the BMEP suffice to prove the general NP-hardness of the FT-BMEP as well as its strong inapproximability.

Suggested Citation

  • Frohn, Martin, 2021. "On the approximability of the Fixed-Tree Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2021020
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