  We provide the first deterministic data structure that given a weighted
undirected graph undergoing edge insertions, processes each update with
polylogarithmic amortized update time and answers queries for the distance
between any pair of vertices in the current graph with a polylogarithmic
approximation in $O(\log \log n)$ time.
  Prior to this work, no data structure was known for partially dynamic graphs,
i.e., graphs undergoing either edge insertions or deletions, with less than
$n^{o(1)}$ update time except for dense graphs, even when allowing
randomization against oblivious adversaries or considering only single-source
distances.
