Engineering Highway Hierarchies

In [1], we presented a shortest path algorithm that allows fast point-to-point queries in graphs using preprocessed data. Here, we give an extensive revision of our method. It allows faster query and preprocessing times, it reduces the size of the data obtained during the preprocessing and it deals with directed graphs. Some important concepts like the

neighbourhood radii

and the

contraction of a network

have been generalised and are now more flexible. The query algorithm has been simplified: it differs only by a few lines from the bidirectional version of

Dijkstra

’s algorithm. We can prove that our algorithm is correct even if the graph contains several paths of the same length.

Experiments with real-world road networks confirm the effectiveness of our approach. Preprocessing the network of Western Europe, which consists of about 18 million nodes, takes 15 minutes and yields 68 bytes of additional data per node. Then, random queries take 0.76 ms on average. If we are willing to accept slower query times (1.38 ms), the memory usage can be decreased to 17 bytes per node. For the European and the US road networks, we can guarantee that at most 0.05% of all nodes are visited during any query.