Engineering multilevel overlay graphs for shortest-path queries

An overlay graph of a given graph G = (V, E) on a subset S ⊆ V is a graph with vertex set S and edges corresponding to shortest paths in G. In particular, we consider variations of the multilevel overlay graph used in Schulz et al. [2002] to speed up shortest-path computation. In this work, we follow up and present several vertex selection criteria, along with two general strategies of applying these criteria, to determine a subset S of a graph's vertices. The main contribution is a systematic experimental study where we investigate the impact of selection criteria and strategies on multilevel overlay graphs and the resulting speed-up achieved for shortest-path computation: Depending on selection strategy and graph type, a centrality index criterion, selection based on planar separators, and vertex degree turned out to perform best.

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