Covering problems

In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another, or how large the structure has to be to do that. Covering problems are minimization problems and usually linear programs, whose dual problems are called packing problems.

The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem.

In the context of linear programming, one can think of any linear program as a covering problem if the coefficients in the constraint matrix, the objective function, and right-hand side are nonnegative. More precisely, let us consider the following general integer linear program:

Such an integer linear program is called covering problem if ${\displaystyle a_{ij},b_{j},c_{i}\geq 0}$ for all ${\displaystyle i=1,\dots ,n}$ and ${\displaystyle j=1,\dots ,m}$.

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