Before revision:  We observe that a small modification of the online covering framework by Buchbinder and Naor implies a polynomial-time primal-dual approach with separation oracles, which a priori might perform exponentially many calls to the oracle .
After revision:  We observe that a small modification of the online covering framework by Buchbinder and Naor implies a polynomial-time primal-dual approach with separation oracles, which a priori might perform exponentially many calls .