  A high number of discrete optimization problems, including Vertex Cover, Set
Cover or Feedback Vertex Set, can be unified into the class of covering
problems. Several of them were shown to be inapproximable by deterministic
algorithms. This article proposes a new random approach, called Choose
Outsiders First, which consists in selecting randomly ele- ments which are
excluded from the cover. We show that this approach leads to random outputs
which mean size is at most twice the optimal solution.
