Orphan diseases are ones that affect very few people. For that reason, there may be no drugs specifically aimed at them, so one tries cocktails of drugs designed for other related diseases. One difficulty with cocktails is that drugs can interact badly. On the other hand, if drugs do not interact badly there is no reason not to try them together in the hopes of gaining a synergistic effect.
Mathematically, the drugs are nodes and harmful interactions are edges between drugs. Given such an undirected graph, the goal to find all maximal cocktails, which correspond to maximum independent sets.
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