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On the approximability of the fixed-tree balanced minimum evolution problem.

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.

SUBMITTER: Frohn M

PROVIDER: S-EPMC7778423 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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On the approximability of the fixed-tree balanced minimum evolution problem.

Frohn Martin M

Optimization letters 20210102 6

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 g ...[more]

PMID: 33425038

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