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Hyperbolicity is a graph parameter related to how much a graph resembles atree with respect to distances. Its computation is challenging as the mainapproaches consist in scanning all quadruples of the graph or using fast matrixmultiplication as building block, both are not practical for large graphs. Inthis paper, we propose and evaluate an approach that uses a hierarchy ofdistance-k dominating sets to reduce the search space. This technique, comparedto the previous best practical algorithms, enables us to compute thehyperbolicity of graphs with unprecedented size (up to a million nodes) andspeeds up the computation of previously attainable graphs by up to 3 orders ofmagnitude while reducing the memory consumption by up to more than a factor of23.

Hyperbolicity Computation through Dominating Sets