Heuristic algorithms for best match graph editing

Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics as a representation of the pairwise most closely related genes among multiple species. An arc connects a gene x with a gene y from another species (vertex color) Y whenever it is one of the phylogenetically closest relatives of x. BMGs can be approximated with the help of similarity measures between gene sequences, albeit not without errors. Empirical estimates thus will usually violate the theoretical properties of BMGs. The corresponding graph editing problem can be used to guide error correction for best match data. 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 (binary trees on three vertices) defined on the set of genes, 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.

Noisy BMG data can be corrected with sufficient accuracy and efficiency to make BMGs an attractive alternative to classical phylogenetic methods.