The current widespread use of location-based services and GPS technologies has revived interest in very fast and scalable shortest path queries. We introduce a new shortest path query type in which dynamic constraints may be placed on the allowable set of edges that can appear on a valid shortest path (e.g., dynamically restricting the type of roads or modes of travel which may be considered in a multimodal transportation network). We formalize this problem as a specific variant of formal language constrained shortest path problems, which we call the Kleene Language Constrained Shortest Paths problem. To efficiently support this type of dynamically constrained shortest path query for large-scale datasets, we extend the hierarchical graph indexing technique known as Contraction Hierarchies. Our experimental evaluation using the North American road network dataset (with over 50 million edges) shows an average query speed and search space improvement of over 3 orders of magnitude compared to the naïve adaptation of the standard Dijkstra's algorithm to support this query type. We also show an improvement of over 2 orders of magnitude compared to the only previously-existing indexing technique which could solve this problem without additional preprocessing.

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In this work, we explore a new type of flexible shortest-path query, in which the query can be dynamically parameterized to constrain the type of edges that may be included in the resulting shortest path (e.g., find the shortest path in a road network that avoids toll roads and low overpasses, respective of the specified vehicle height). We extend the hierarchical preprocessing technique known as Contraction Hierarchies to efficiently support such flexible queries. We also present several effective algorithmic optimizations for further improving the overall scalability and query times of this approach, including the addition of goaldirected search techniques, search space pruning techniques, and generalizing the constraints of the local search. Experiments are presented for both the North American and the European road networks, showcasing the general effectiveness and scalability of our proposed methodology to large-scale, real-world graphs.