Hyperbolicity Computation through Dominating Sets

David Coudert (1) , André Nusser (2) , Laurent Viennot (3, 4)

1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
2 Max Planck Institute for Informatics [Saarbrücken]
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
4 Inria de Paris

Hyperbolicity is a graph parameter related to how much a graph resembles a tree with respect to distances. Its computation is challenging as the main approaches consist in scanning all quadruples of the graph or using fast matrix multiplication as building block, both are not practical for large graphs. In this paper, we propose and evaluate an approach that uses a hierarchy of distance-k dominating sets to reduce the search space. This technique, compared to the previous best practical algorithms, enables us to compute the hyperbolicity of graphs with unprecedented size (up to a million nodes) and speeds up the computation of previously attainable graphs by up to 3 orders of magnitude while reducing the memory consumption by up to more than a factor of 23.

Mots clés: Gromov hyperbolicity; Graph algorithms; Algorithm engineering

Domaines: Réseaux et télécommunications [cs.NI]; Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

David Coudert, André Nusser, Laurent Viennot. Hyperbolicity Computation through Dominating Sets. ALENEX 2022 - SIAM Symposium on Algorithm Engineering and Experiments, Jan 2022, Alexandria, VA, United States. pp.78-90, ⟨10.1137/1.9781611977042.7⟩. ⟨hal-03431155v2⟩