Tight approximation for unit-cost and unit-profit variants

Determine whether MinMax-Pack with unit costs or MaxMin-Cov with unit profits admits an o(n)-approximation, or prove that the inapproximability lower bound can be strengthened to n^{1-o(1)}.

Background

The paper establishes that unit-cost MinMax-Pack and unit-profit MaxMin-Cov admit an n-approximation, while no polynomial-time n^{1-ε}-approximation exists for any fixed ε>0 unless P=NP. These results determine the polynomial exponent of the approximation threshold but leave a subpolynomial gap between the known upper and lower bounds. The unresolved issue is whether the factor can be improved below n by a subpolynomial amount, or whether hardness persists essentially up to the linear factor.