Is it possible to approximate a monotone submodular function using a concrete coverage function, i.e.

Given a ground set $U$ and a monotone submodular function, $f:2^U\to \mathbb{R}$, the goal is to find another ground set, $V$, and map each element from $U$ to a subset of $V$ ($m:U \to 2^V$) such that $f(S) \leq g(S) \leq \alpha f(S)$ for every $S \subseteq U$, where $\alpha$ is the approximation ratio (hopefully a constant) and $g(S) = c|\bigcup_{e \in S}m(e)|$ for some constant $c$.

An approximation that uses a weighted ground set, $V$, is also very welcomed (I guess we can't avoid that).

Thank you


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.