Set Cover Problem - Integer Linear Program Formulation

Integer Linear Program Formulation

The minimum set cover problem can be formulated as the following integer linear program (ILP).

minimize (minimize the total cost)
subject to for all (cover every element of the universe)
for all . (every set is either in the set cover or not)

This ILP belongs to the more general class of ILPs for covering problems. The integrality gap of this ILP is at most, so its relaxation gives a factor- approximation algorithm for the minimum set cover problem (where is the size of the universe).

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