Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs

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Abstract

In this paper, we consider Dijkstra’s algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.

This work was partially supported by the Human Potential Programme of the European Union under contract no. HPRN-CT-1999-00104 (AMORE) and and by the DFG under grant WA 654/12-1.