Logarithmic inapproximability of the radio broadcast problem

We show that the radio broadcast problem is Ω(log n)-inapproximable unless NP ⊆ BPTIME(nO(log logn)). This is the first result on the hardness of approximation of this problem. Our reduction is based on the reduction from the Label-Cover problem to the Set Cover problem due to Lund and Yannakakis [LY94], and uses some new ideas. Department of Computer Science, Yale University, New Haven, CT, USA, 06520-8285, [email protected]. Part of this work was done in School of Mathematics, Institute for Advanced Study, Princeton, NJ, USA, 08540. Computer Science department, Rutgers University, Camden, NY, USA. Email: [email protected]