Geographic Routing Using Hyperbolic Space

By Robert D. Kleinberg. IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications, 2007

393 citations recorded by the source corpus.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/f506b2ddb142d2ec539400297ba53383d958abef

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In Computer Networks and Communications

Citations in the corpus

Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking (2009, background): “Kleinberg has extended this work and shown that every connected finite graph has a greedy embedding in the hyperbolic plane (Kleinberg, 2007).”
Poincaré Embeddings for Learning Hierarchical Representations (2017, background): “For instance, Kleinberg [18] introduced hyperbolic geometry for greedy routing in geographic communication networks.”
On the Equivalence between Positional Node Embeddings and Structural Graph Representations (2019, neutral): “borrows from deﬁnitions of graph (node) embeddings in metric spaces: a measure of relative node closeness (Abraham et al., 2006; Bourgain, 1985; Cand`es & Recht, 2009; Graham & Winkler, 1985; Kleinberg, 2007; Linial et al., 1995; Rabinovich & Raz, 1998; Recht et al., 2010; Shaw et al., 2”
Machine Learning on Graphs: A Model and Comprehensive Taxonomy (2020, background): “In particular, hyperbolic geometry—a non-Euclidean geometry with a constant negative curvature—is well-suited to represent hierarchical data and has been considered for network science problems [63, 65, 88].”
Low Distortion Delaunay Embedding of Trees in Hyperbolic Plane (2011, methodology): “Kleinberg [12] considers the problem of greedy routing in wireless networks.”
Representation Tradeoffs for Hyperbolic Embeddings (2018, methodology): “Earlier efforts proposed using hyperbolic spaces for routing, starting with Kleinberg’s work on geographic routing (Kleinberg, 2007).”
Chordality and hyperbolicity of a graph (2009, background): “This concept not only turns out to be strikingly useful in coarse geometry but also becomes more and more important in many applied fields like networking and phylogenetics [24, 25, 26, 27, 39, 41, 42, 43, 45, 53, 69, 70, 73, 88].”
Hyperbolic Graph Neural Networks (2019, background): “Furthermore, [27, 6, 28] exploited the property of hyperbolic embeddings to embed tree-like graphs with low distortion, for greedy-path routing in large-scale communication networks.”
Hyperbolic Graph Convolutional Neural Networks (2019, methodology): “Shallow embedding methods have also been developed in hyperbolic geometry [29, 30] for reconstructing trees [35] and graphs [5, 13, 22], or embedding text”