  We design fast deterministic algorithms for distance computation in the
congested clique model. Our key contributions include:
  -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in
$O(\log^2{n} / \epsilon)$ rounds on unweighted undirected graphs. With a small
additional additive factor, this also applies for weighted graphs. This is the
first sub-polynomial constant-factor approximation for APSP in this model.
  -- A $(1+\epsilon)$-approximation for multi-source shortest paths from
$O(\sqrt{n})$ sources in $O(\log^2{n} / \epsilon)$ rounds on weighted
undirected graphs. This is the first sub-polynomial algorithm obtaining this
approximation for a set of sources of polynomial size.
  Our main techniques are new distance tools that are obtained via improved
algorithms for sparse matrix multiplication, which we leverage to construct
efficient hopsets and shortest paths. Furthermore, our techniques extend to
additional distance problems for which we improve upon the state-of-the-art,
including diameter approximation, and an exact single-source shortest paths
algorithm for weighted undirected graphs in $\tilde{O}(n^{1/6})$ rounds.
