Consider the following integer program (general covering):
$\min c \cdot x$ subject to
$Ax \ge b$,
where all entries in $A, b, c$ are nonnegative and $x$ is required to be nonnegative and integral.
In Vazirani, it is an exercise to show that an $O( \log n )$-approximation algorithm exists, where $A$ is an $n$ by $m$ matrix. Could someone give me a reference on how to do this?
In particular, I am interested in the case when $x$ is required to be binary, and in the use of linear programming to approximate.