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arXiv · 1803.10989

Best Match Graphs

Manuela Geiß·Edgar Chavez·Marcos Gonzalez·Alitzel Lopez·Bärbel M. R. Stadler·Dulce I. Valdivia·Marc Hellmuth·Maribel H. Rosales·Peter F. Stadler
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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 $T$ be a phylogenetic (gene) tree $T$ and $σ$ an assignment of leaves of $T$ to species. The best match graph $(G,σ)$ 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 $σ(y)$. Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether $(G,σ)$ derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains $(G,σ)$, which can also be constructed in cubic time.

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Manuela Geiß, Edgar Chavez, Marcos Gonzalez, Alitzel Lopez, Bärbel M. R. Stadler, Dulce I. Valdivia, Marc Hellmuth, Maribel H. Rosales, Peter F. Stadler. 2020-09-09. Best Match Graphs. https://doi.org/10.1007/s00285-019-01332-9

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