High-Performance Multi-Level Graphs

Shortest-path computation is a frequent task in practice. Owing to ever-growing realworld graphs, there is a constant need for faster algorithms. In the course of time, a large number of techniques to heuristically speed up Dijkstra’s shortest-path algorithm have been devised. This work reviews the multi-level technique to answer shortest-path queries exactly [1, 2], which makes use of a hierarchical decomposition of the input graph and precomputation of supplementary information. We develop this preprocessing to the maximum and introduce several ideas to enhance this approach considerably, by reorganizing the precomputed data in partial graphs and optimizing them individually. To answer a given query, certain partial graphs are combined to a search graph, which can be explored by a simple and fast procedure. The concept behind the construction of the search graph is such that query times depend mainly on the number of partial graphs included. This is confirmed by experiments with a road graph containing over 15 million vertices. Our query algorithm computes the distance for any pair of vertices in no more than 70 μs. However, a lengthy preprocessing is required to achieve this query performance.