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

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