TL;DR
This paper characterizes best match graphs used in orthology detection, providing algorithms to recognize and reconstruct the unique minimal phylogenetic tree explaining such graphs efficiently.
Contribution
It offers a complete characterization of best match graphs and presents algorithms for recognition and tree reconstruction in polynomial time.
Findings
Recognition of best match graphs can be decided in cubic time.
A unique least resolved tree explains each best match graph, constructed in cubic time.
The study formalizes the structure of best match graphs in phylogenetics.
Abstract
THIS IS A CORRECTED VERSION INCLUDING AN APPENDED CORRIGENDUM. Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let be a phylogenetic (gene) tree and an assignment of leaves of to species. The best match graph is a digraph that contains an arc from to if the genes and reside in different species and is one of possibly many (evolutionary) closest relatives of compared to all other genes contained in the species . Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains , which can also be constructed in cubic time.
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