2020/11/01 by Schaller, David, Geiß, Manuela, Hellmuth, Marc +1 · 1 citation
#Combinatorics (math.CO) #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE)
paper · doi:10.48550/arxiv.2011.00511
Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine whether a BMG is binary-explainable, i.e., whether it can be explained by a fully resolved gene tree and, if so, to construct such a tree. Moreover, we show that all such binary trees are refinements of the unique binary-resolvable tree (BRT), which in general is a substantial refinement of the also unique least resolved tree of a BMG. Finally, we show that the problem of editing an arbitrary vertex-colored graph to a binary-explainable BMG is NP-complete and provide an integer linear program formulation for this task.