We propose an approximation method to answer shortest path queries in graphs, based on hierarchical random sampling and Voronoi duals. The lowest level of the hierarchy stores the initial graph. At each higher level, we compute a simplification of the graph on the level below, by selecting a constant fraction of nodes. Edges are generated as the Voronoi dual within the lower level, using the selected nodes as Voronoi sites. This hierarchy allows for fast computation of approximate shortest paths for general graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths.
Sommer et al. (2008) studied this question.
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