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Strongly Hyperbolic Unit Disk Graphs

Bläsius, Thomas ORCID iD icon 1; Friedrich, Tobias; Katzmann, Maximilian 2; Stephan, Daniel
1 Institut für Theoretische Informatik (ITI), Karlsruher Institut für Technologie (KIT)
2 Karlsruher Institut für Technologie (KIT)

Abstract:

The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant. In contrast to the grid-like structures exhibited by Euclidean unit disk graphs, strongly hyperbolic networks feature hierarchical structures, which are also observed in complex real-world networks.
We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to demonstrate that the class is useful for the development and analysis of graph algorithms. Specifically, we develop a simple greedy routing scheme and analyze its performance on strongly hyperbolic unit disk graphs in order to prove that routing can be performed more efficiently on such networks than in general.


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Originalveröffentlichung
DOI: 10.4230/lipics.stacs.2023.13
Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2023
Sprache Englisch
Identifikator ISBN: 978-3-9597726-6-2
ISSN: 1868-8969
KITopen-ID: 1000157578
Verlag Schloss Dagstuhl - Leibniz-Zentrum für Informatik (LZI)
Serie 254
Schlagwörter hyperbolic geometry, unit disk graphs, greedy routing, hyperbolic random graphs, graph classes, Theory of computation → Graph algorithms analysis, Theory of computation → Computational geometry, Mathematics of computing → Graph algorithms
Nachgewiesen in Scopus
arXiv
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