Before revision:  For any (randomized) algorithm, there are input graphs with n nodes and maximum degree \Delta on which \Omega(\min\{\log n/\log \log n,\log \Delta/\log \log \Delta\}) (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching , respectively . Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings.
After revision:  For any (randomized) algorithm, there are input graphs with n nodes and maximum degree \Delta on which \Omega(\min\{\log n/\log \log n,\log \Delta/\log \log \Delta\}) (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching . Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings.