  We present the first approximate distance oracle for sparse directed networks
with time-dependent arc-travel-times determined by continuous, piecewise
linear, positive functions possessing the FIFO property.
  Our approach precomputes $(1+\epsilon)-$approximate distance summaries from
selected landmark vertices to all other vertices in the network. Our oracle
uses subquadratic space and time preprocessing, and provides two sublinear-time
query algorithms that deliver constant and $(1+\sigma)-$approximate
shortest-travel-times, respectively, for arbitrary origin-destination pairs in
the network, for any constant $\sigma > \epsilon$. Our oracle is based only on
the sparsity of the network, along with two quite natural assumptions about
travel-time functions which allow the smooth transition towards asymmetric and
time-dependent distance metrics.
