Partition-Based Speed-Up of Dijkstra’s Algorithm

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 the smallest search space for Dijkstra’s algorithm for most of the tested street networks. This paper was presented as ”Studienarbeit” at the university of Karlsruhe (TH) at the institute of Prof. Dr. D. Wagner. I would like to thank Thomas Willhalm and Heiko Schilling for this interesting topic, their ideas and help. Hiermit versichere ich, dass ich die vorliegende Arbeit selbständig angefertigt habe und nur die angegebenen Hilfsmittel und Quellen verwendet wurden. Karlsruhe, im November 2004