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Details about my sets:
each set have exactly M elements, and each element belongs to exactly N sets.
I need a Non greedy algorithm to compute the size of the minimal set cover.
is there a good algorithm? (for my special case)
thanks.
The hardness results and probably the inapproximability results (perhaps with a worse constant) apply even to your special case. Use a solver for mixed-integer programs such as GLPK.