Engineering Generalized Shortest Path Queries

Generalized Shortest Path (GSP) queries represent a variant of constrained shortest path queries in which a solution path of minimum total cost must visit at least one location from each of a set of specified location categories (e. g., gas stations, grocery stores) in a specified order. This problem type has many practical applications in logistics and personalized location-based services, and is closely related to the NP-hard Generalized Traveling Salesman Path Problem (GTSPP). In this work, we present a new dynamic programming formulation to highlight the structure of this problem. Using this formulation as our foundation, we progressively engineer a fast and scalable GSP query algorithm for use on large, real-world road networks. Our approach incorporates concepts from Contraction Hierarchies, a well-known graph indexing technique for static shortest path queries. To demonstrate the practicality of our algorithm we experimented on the North American road network (with over 50 million edges) where we achieved up to several orders of magnitude speed improvements over the previous-best algorithm, depending on the relative sizes of the location categories.