During the last years, several speed-up techniques for Dijkstra’s algorithm have been published that maintain the correctness of the algorithm but reduce its running time for typical instances. They are usually based on a preprocessing that annotates the graph with additional information which can be used to prune or guide the search. Timetable information in public transport is a traditional application domain for such techniques. In this paper, we provide a condensed overview of new developments and extensions of classic results. Furthermore, we discuss how combinations of speed-up techniques can be realized to take advantage from different strategies.

Determining the shortest path from one node to another in a graph is probably the most popular question in graph theory. If the graph is non-negatively weighted, Dijkstra’s algorithm is the classic algorithm used to answer this question. Because of its breadth-first-search character, this algorithm usually spreads circularly around the source node of the search and hence the search space can be very large. For the application of dealing with huge numbers of shortest-path queries in static graphs, we consider an algorithm, which uses preprocessed data to decrease the search space for each shortest-path request. The algorithm partitions the graph and, for each edge, the preprocessing considers the relevant regions which have the shortest path over this edge. We will see that the preprocessing scales well and usually runs in almost linear time. This document shows experimental results for several partitioning algorithms resulting in smaller search spaces on real-world street networks. The quality of these strategies will be compared. A two-level kd-tree with bidirectional search delivered