Before revision:  Contributing to this line of work on MPC graph algorithms, we present \text{poly (\log k) \in \text{poly (\log\log n) round MPC algorithms for computing O(k^{1+{o(1)}})-spanners in the strongly sublinear regime of local memory.
After revision:  Contributing to this line of work on MPC graph algorithms, we present \text{poly (\log k) \in poly (\log\log n) round MPC algorithms for computing O(k^{1+{o(1)}})-spanners in the strongly sublinear regime of local memory.