An Axiomatic Approach to Time-Dependent Shortest Path Oracles

Computing shortest paths in networks that exhibit a time-dependent metric is a core routine for many applications, with route planning in road networks being a prime example. In this work, we present an axiomatic approach which shows that for directed networks that satisfy certain properties we can provide time-dependent distance oracles that provably exhibit subquadratic preprocessing time and space (independent of the metric’s amount of disconcavity), query time sublinear on the network size or the actual Dijkstra rank of the query at hand (measuring the distance ordering of the destination from the origin), and small stretch factor (approximation error).