- takes as input: 1. a set of elements/vertices $U$ 2. sets $S_1, ..., S_n \subseteq U$ - outputs a selection of $S_i$ whose union is $U$, with the minimum number of sets picked (optimization) - (covers all elements) ![[CleanShot 2024-05-09 at 11.38.55.png|200x200]] - has approximate solution with [[Set Cover Greedy Algorithm]] https://people.eecs.berkeley.edu/~vazirani/algorithms/chap5.pdf https://www.geeksforgeeks.org/set-cover-is-np-complete/#