Best Match Graphs

Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let T be a phylogenetic (gene) tree T and \(\sigma \) an assignment of leaves of T to species. The best match graph \((G,\sigma )\) is a digraph that contains an arc from x to y if the genes x and y reside in different species and y is one of possibly many (evolutionary) closest relatives of x compared to all other genes contained in the species \(\sigma (y)\). Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether \((G,\sigma )\) derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains \((G,\sigma )\), which can also be constructed in cubic time.