I have a $k-$uniform hypergraph $H=(V,E)$ with $n$ vertices. I need to partition $H$ into two partitions of sizes $r$ and $n-r$. Is there an approximating algorithm that can do this while minimizing conductance?
I do not care about the time complexity as long as it is not exponential. Also, if there is no global algorithm I would be satisfied with a local one.
Additional info: My actual reason for selecting conductance as the minimization objective is because I want to increase the quantity $\frac{|E(R)|}{|E'(R)|}$ where $R$ is the set made up of the $r$ vertices, $|E(R)|$ is the total number of hyperedges that are fully inside $R$ and $|E'(R)|$ is the total cut edges. Since $vol(R)=k|E(R)|+|E'(R)|$ in a $k-$uniform hypergraph, this will be equivalent to maximizing $\left(\frac{vol(R)}{|E'(R)|}-1\right)\frac{1}{k}$. And, $\frac{|E'(R)|}{vol(R)}$ is the conductance.
