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I guess you speak about the "set cover problem", which is a well known NP-hard problem (Karp). Sage does not have this though it could be added as a method of IncidenceStructure.
You can however code it yourself :
- look at the
MixedIntegerProgrammingexamples and tutorial - note that sets are not hashable, so a MIP variable could not be indexed by sets. However, if your sets belong to a list, you just have to index them by their position in the list.
