# Approximate Multi Covering with Randomized Rounding

In the set multicover problem we are given a set $$N$$ of $$n$$ elements and a set $$S$$ of $$m$$ subsets of $$N$$. Additionally, each element has a coverage requirement (the number of times it has to be covered) and each set has a weight. The question is to cover $$N$$ with the minimum weight subsets from $$S$$. I'm aware of the approximation algorithm for this problem using (Rajagopalan & Vazirani) .

But I am interested in finding an algorithm for this problem that uses the randomized rounding and study its approximation factor.