# Covering problem

### From Glossary

The idea is to select enough members in each of a specified collection of sets; that defines
*covering the sets*. Subject to this, there is a cost for the elements selected, and the objective is to minimize total cost. The IP form of the usual set covering problem is

where if element is selected; else, . The matrix has 0's and 1's, where the -th row corresponds to the -th set to be covered: means element is in set ; else, . The constraint means that at least one element of each set must be selected. This could be extended to require elements of set be selected by writing . Also see vertex cover.