HyperANF: Approximating the Neighbourhood Function of Very Large Graphs on a Budget

The neighbourhood function NG(t) of a graph G gives, for each t ∈ N, the number of pairs of nodes x, y such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph [PGF02] (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm [PGF02] (approximate neighbourhood function) has been proposed with the purpose of approximating NG(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters [FFGM07] and combines them efficiently through broadword programming [Knu07]; our implementation uses overdecomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small error and good confidence using a standard workstation. Then, w...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Paolo Boldi, Marco Rosa, Sebastiano Vigna
• Keywords: Approximate Neighbourhood Function, CORR 2010, Education, Neighbourhood Function, Neighbourhood Function Ng