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+ϵ)−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+σ)−approximate
shortest-travel-times, respectively, for arbitrary origin-destination pairs in
the network, for any constant σ>ϵ. 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.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of
EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An
extended abstract also appeared in the 41st International Colloquium on
Automata, Languages, and Programming (ICALP 2014, track-A