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On computing the Gromov hyperbolicity

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Title: On computing the Gromov hyperbolicity
Authors: Cohen, Nathann, Coudert, David, Lancin, Aurélien
Contributors: Laboratoire de Recherche en Informatique (LRI), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Combinatorics, Optimization and Algorithms for Telecommunications (COATI), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (. - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (. - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-13-BS02-0007,Stint,Structures Interdites(2013), ANR-11-LABX-0031,UCN@SOPHIA,Réseau orienté utilisateur(2011), European Project: 258307,EC:FP7:ICT,FP7-ICT-2009-5,EULER(2010)
Source: ISSN: 1084-6654 ; ACM Journal of Experimental Algorithmics ; https://hal.inria.fr/hal-01182890 ; ACM Journal of Experimental Algorithmics, Association for Computing Machinery, 2015, 20 (1), pp.18. ⟨10.1145/2780652⟩.
Publisher Information: HAL CCSD
Association for Computing Machinery
Publication Year: 2015
Collection: Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
Subject Terms: Algorithms, Gromov Hyperbolicity, Networks, ACM: G.: Mathematics of Computing/G.2: DISCRETE MATHEMATICS/G.2.2: Graph Theory, ACM: G.: Mathematics of Computing/G.2: DISCRETE MATHEMATICS/G.2.2: Graph Theory/G.2.2.0: Graph algorithms, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
Description: International audience ; The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree. It is for instance used to provide bounds on the expected stretch of greedy-routing algorithms in Internet-like graphs. However, the best known theoretical algorithm computing this parameter runs in O(n^3.69) time, which is prohibitive for large-scale graphs. In this paper, we propose an algorithm for determining the hyperbolicity of graphs with tens of thousands of nodes. Its running time depends on the distribution of distances and on the actual value of the hyperbolicity. Although its worst case runtime is O(n^4), it is in practice much faster than previous proposals as observed in our experimentations. Finally, we propose a heuristic algorithm that can be used on graphs with millions of nodes. Our algorithms are all evaluated on benchmark instances.
Document Type: article in journal/newspaper
Language: English
Relation: info:eu-repo/grantAgreement/EC/FP7/258307/EU/Experimental UpdateLess Evolutive Routing/EULER; hal-01182890; https://hal.inria.fr/hal-01182890; https://hal.inria.fr/hal-01182890/document; https://hal.inria.fr/hal-01182890/file/CCL15-no-format.pdf
DOI: 10.1145/2780652
Availability: https://hal.inria.fr/hal-01182890
https://hal.inria.fr/hal-01182890/document
https://hal.inria.fr/hal-01182890/file/CCL15-no-format.pdf
https://doi.org/10.1145/2780652
Rights: info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.C5A2FC2B
Database: BASE
Description
Abstract:International audience ; The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree. It is for instance used to provide bounds on the expected stretch of greedy-routing algorithms in Internet-like graphs. However, the best known theoretical algorithm computing this parameter runs in O(n^3.69) time, which is prohibitive for large-scale graphs. In this paper, we propose an algorithm for determining the hyperbolicity of graphs with tens of thousands of nodes. Its running time depends on the distribution of distances and on the actual value of the hyperbolicity. Although its worst case runtime is O(n^4), it is in practice much faster than previous proposals as observed in our experimentations. Finally, we propose a heuristic algorithm that can be used on graphs with millions of nodes. Our algorithms are all evaluated on benchmark instances.
DOI:10.1145/2780652