Dynamic Shortest Paths Containers

Using a set of geometric containers to speed up shortest path queries in a weighted graph has been proven a useful tool for dealing with large sparse graphs. Given a layout of a graph G = (V; E), we store, for each edge (u; v) 2 E, the bounding box of all nodes t 2 V for which a shortest u-t-path starts with (u; v). Shortest path queries can then be answered by Dijkstra’s algorithm restricted to edges where the corresponding bounding box contains the target. In this paper, we present new algorithms as well as an empirical study for the dynamic case of this problem, where edge weights are subject to change and the bounding boxes have to be updated. We evaluate the quality and the time for dieren t update strategies that guarantee correct shortest paths in an interesting application to railway information systems, using real-world data from six European countries.

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