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Set cover is a well-known NP-complete problem: given a collection of sets, find as small as possible a subcollection whose union is the same as the union of the entire collection.

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Counterexample to greedy solution for set cover problem

Usually the set cover problem is formulated such that the quantity to be minimized is the number of sets one picks rather than the sum of the numbers of elements of the sets picked. Unfortunately, thi …
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