• I guess one can think of the ARV algorithm to be giving a polynomial time $$O(\sqrt{log (n)})$$-approximation algorithm to get the Cheeger constant. Right?
• Now consider the quantity, $$N-cut = \sum_{i=1}^{k} \frac { E(S_i,V /\ S_i)}{Vol(S_i) }$$ where $$S_i$$ are $$k$$ disjoint sets partitioning the graph and $$Vol(S_i)$$ is the sum of the degrees of the vertices in $$S_i$$.
Does the ARV algorithm automatically also give an approxmation algorithm for finding the sets $$S_i$$ which will give the lowest value of N-cut? (if not, then what is the best known answer to this?)