Theoretical Computer Science Stack Exchange is a question and answer site for theoretical computer scientists and researchers in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am wondering if this is a studied variant of the Set Cover problem.

We are given a universe $X$, a collection of sets $S = \{S_1, ..., S_m\}$ and integers $c_i$. We want to cover all elements in $X$ with sets $S'_i \subseteq S_i$ such that $|S'_i| \leq c_i$. In other words we want to cover the elements with as few sets as possible but we are only allowed to use $c_i$ elements of each set.

The most similar variant I found is described in "Maximum Coverage Problem with Group Budget Constraints and Applications"

Thank you

share|cite|improve this question

Yes, this variant, and in fact a further generalization has been considered in the literature. See the paper below for the problem they call capacitated facility location.

J. Bar-Ilan, G. Kortsarz and D. Peleg, Generalized submodular cover problems and applications, Theoretical Computer Science, 250:179-200, 2001.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.