Enumerating maximal bicliques in bipartite graphs with favorable degree sequences
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The evolutionary histories of viral genomes have received significantrecent attention due to their importance in understanding virulenceand the corresponding ramifications to public health. We present anovel framework to detect reassortment events in influenza based onthe comparison of two distributions of phylogenetic trees, rather thana pair of, possibly unreliable, consensus trees. We show how to detectall high-probability inconsistencies between two distributions oftrees by enumerating maximal bicliques within a definedincompatibility graph. In the process, we give the first quadraticdelay algorithm for enumerating maximal bicliques within generalbipartite graphs. We demonstrate the utility of our approach byapplying it to several sets of influenza genomes (both human- andavian-hosted) and successfully identify all known reassortment eventsand a few novel candidate reassortments. In addition, on simulateddatasets, our approach correctly finds implanted reassortments andrarely detects reassortments where none were introduced.