Interactive proofs and approximation: reductions from two provers in one round

The author presents hard to approximate problems in the following areas: systems of representatives, network flow, and longest paths in graphs. In each case he shows that there exists some delta >0 such that polynomial time approximation to within a factor of 2/sup log delta n/ of the optimal implies that NP has quasi polynomial time deterministic simulations. The results are derived by reduction from two prover, one round proof systems, and exemplify the ability of such reductions to yield hardness of approximations results for many different kinds of problems.<>