Before revision:  We also devise efficient algorithms for computing (\le \le 1 +\epsilon)-approximate shortest paths from each vertex to its k nearest neighbors in directed graphs.
After revision:  In the Congested Clique model, our algorithm solves the problem in polylogarithmic time for |S| = n^r sources, for r\le \le 1 +\epsilon)-approximate shortest paths from each vertex to its k nearest neighbors in directed graphs.