Before revision:  To the best of our knowledge, these are the first sublogarithmic-time MPC algorithms for computing spanners and distance approximation .
After revision:  To the best of our knowledge, these are the first sublogarithmic-time MPC algorithm for distance approximations. -Our result above also extends to the Congested Clique model of distributed computing, with the same round complexity and approximation guarantee. This gives the first sub-logarithmic algorithm for approximating APSP in weighted graphs in the Congested Clique model .