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Set-Covering Problem

Given a finite set X and a family F of subsets of X, X = \(\bigcup_{S \in
F} S\), find a minimum-size subset C $\subseteq$ F whose members cover all of X.



SC = {$\langle$X, F, k$\rangle$$\mid$ there exists a set cover C $\subseteq$ F covering X with size $\leq$ k}



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