Extracting Small Subgraphs in Road Networks

Online navigation platforms are well optimized to solve the standard objective of minimizing travel time and typically re-quire precomputation-based architectures (such as Contraction Hierarchies and Customizable Route Planning) to do so in a fast manner. The reason for this dependence is the size of the graph that represents the road network, which is large. The need to go beyond minimizing the travel time and introduce various types of customizations has led to approaches that rely on alternative route computation or, more generally, small subgraph extraction. On a small subgraph, one can run computationally expensive algorithms at query time and compute optimal solutions for multiple routing problems. In this framework, it is critical for the subgraph to (a) be small and (b) include (near) optimal routes for a collection of customizations. This is precisely the setting that we study in this work. We design algorithms that extract a subgraph connecting designated terminals with the objective of minimizing the subgraph's size and the constraint of including near-optimal routes for a set of predefined cost functions. We provide theoretical guarantees for our algorithms and evaluate them empirically using real-world road networks.