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Best match graphs. (English) Zbl 1415.92133
J. Math. Biol. 78, No. 7, 2015-2057 (2019); corrigendum ibid. 82, No. 6, Paper No. 47, 9 p. (2021).
Summary: 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.

MSC:
92D15 Problems related to evolution
92D10 Genetics and epigenetics
05C90 Applications of graph theory
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