Sketch-based Algorithms for Approximate Shortest Paths in Road Networks

Constructing efficient data structures (distance oracles) for fast computation of shortest paths and other connectivity measures in graphs has been a promising area of study in computer science [23, 24, 28]. In this paper, we propose very efficient algorithms, based on a distance oracle, for computing approximate shortest paths and alternate paths in road networks. Specifically, we adopt a distance oracle construction that exploits the existence of small separators in such networks. In other words, the existence of a small cut in a graph admits a partitioning of the graph into balanced components with a small number of inter-component edges. We demonstrate the efficacy of our algorithm by using it to find near optimal shortest paths and show that it also has the desired properties of well-studied goal-oriented path search algorithms such as ALT [12]. We further demonstrate the use of our distance oracle to produce multiple alternative routes in addition to the shortest path. Finally, we empirically demonstrate that our method, while exploring few edges, produces high quality alternates with respect to metrics such as optimality-loss and diversity of paths.