Implementations of routing algorithms for transportation networks

We discuss the generalization of the point-to-point (and single-source) shortest path problem to instances where the shortest path must satisfy a formal language constraint. We describe theoretical and experimental results on a generalization of Dijkstra’s algorithm to finding regular-language-constrained shortest paths. This algorithm forms a model for single-source shortest paths and point-to-point problems that generalizes several previously published algorithms for multimodal shortest path problems. The experiments include work with two different implementations. One is the original implementation of the restriction of the problem to linear regular expressions, which formed a part of the TRANSIMS project at the Los Alamos National Laboratory. The other is a new implementation of the general regular-language-constrained shortest path algorithm that uses an implicit representation of the product graph. The second implementation also provides several speed-up techniques which have previously only been used for standard point-to-point shortest path problems. Through our experiments, we study the scalability of the algorithm with respect to the network size as well as with respect to the constraining language complexity. Further, we study the effectiveness of speed-up techniques such as bidirectional search, shortest path containers, bit-vectors and the multilevel technique when applied to the multimodal shortest path problems formalized by the regular language constraints (Some of these are in progress and will be fully described in a more complete version of the paper.)