  Best match graphs (BMGs) are a class of colored digraphs that naturally
appear in mathematical phylogenetics and can be approximated with the help of
similarity measures between gene sequences, albeit not without errors. The
corresponding graph editing problem can be used as a means of error correction.
Since the arc set modification problems for BMGs are NP-complete, efficient
heuristics are needed if BMGs are to be used for the practical analysis of
biological sequence data. Since BMGs have a characterization in terms of
consistency of a certain set of rooted triples, we consider heuristics that
operate on triple sets. As an alternative, we show that there is a close
connection to a set partitioning problem that leads to a class of top-down
recursive algorithms that are similar to Aho's supertree algorithm and give
rise to BMG editing algorithms that are consistent in the sense that they leave
BMGs invariant. Extensive benchmarking shows that community detection
algorithms for the partitioning steps perform best for BMG editing.
