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We propose an approximation method to answer point-to-point shortest path queries in undirected graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoffdoi:10.1109/isvd.2009.30 dblp:conf/isvd/HonidenHSW09 fatcat:7n5gvkparvfm3mhr4xfinm5vea