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We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a hop-doubling labeling technique. We derive bounds on the index size, the computation costs and I/O costs based on the properties of unweighted scale-free graphs. We show that our method is much more efficient compared to the state-of-the-art technique, in terms of both querying time and indexing time. Our empirical study shows that our method can handle graphs that are orders of magnitude larger than existing methods.
Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$ of nodes
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