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Hyperbolic Embeddings for Near-Optimal Greedy Routing

Authors:

Thomas Bläsius,

Tobias Friedrich,

Maximilian Katzmann,

Anton KrohmerAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 25

Article No.: 1.3, Pages 1 - 18

https://doi.org/10.1145/3381751

Published: 20 March 2020 Publication History

Abstract

Greedy routing computes paths between nodes in a network by successively moving to the neighbor closest to the target with respect to coordinates given by an embedding into some metric space. Its advantage is that only local information is used for routing decisions. We present different algorithms for generating graph embeddings into the hyperbolic plane that are well suited for greedy routing. In particular, our embeddings guarantee that greedy routing always succeeds in reaching the target, and we try to minimize the lengths of the resulting greedy paths.

We evaluate our algorithm on multiple generated and real-world networks. For networks that are generally assumed to have a hidden underlying hyperbolic geometry, such as the Internet graph [3], we achieve near-optimal results (i.e., the resulting greedy paths are only slightly longer than the corresponding shortest paths). In the case of the Internet graph, they are only 6% longer when using our best algorithm, which greatly improves upon the previous best known embedding, whose creation required substantial manual intervention.

In addition to measuring the stretch, we empirically evaluate our algorithms regarding the size of the coordinates of the resulting embeddings and observe how it impacts the success rate when coordinates are not represented with very high precision. Since numerical difficulties are a major issue when performing computations in the hyperbolic plane, we consider variations of our algorithm that improve the success rate when using coordinates with lower precision.

References

[1]

Xiaomeng Ban, Jie Gao, and Arnout van de Rijt. 2010. Navigation in real-world complex networks through embedding in latent spaces. In Proceedings of the Meeting on Algorithm Engineering and Expermiments (ALENEX’10). 138--148.

[2]

Thomas Bläsius, Tobias Friedrich, Anton Krohmer, and Sören Laue. 2016. Efficient embedding of scale-free graphs in the hyperbolic plane. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), P. Sankowski and C. Zaroliagis (Eds.), Vol. 57. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, Article 16, 18 pages.

[3]

Marián Boguñá, Fragkiskos Papadopoulos, and Dmitri Krioukov. 2010. Sustaining the Internet with hyperbolic mapping. Nature Communications 1 (2010), 62.

[4]

Michele Borassi and Emanuele Natale. 2016. KADABRA is an ADaptive algorithm for betweenness via random approximation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), P. Sankowski and C. Zaroliagis (Eds.), Vol. 57. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, Article 20, 18 pages.

[5]

A. Cvetkovski and M. Crovella. 2009. Hyperbolic embedding and routing for dynamic graphs. In Proceedings of the 28th IEEE International Conference on Computer Communications (IEEE INFOCOM’09). 1647--1655.

[6]

David Eppstein and Michael T. Goodrich. 2011. Succinct greedy geometric routing using hyperbolic geometry. IEEE Transactions on Computers 60, 11 (2011), 1571--1580.

Digital Library

[7]

Laurent Fousse, Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, and Paul Zimmermann. 2007. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Transactions on Mathematical Software 33, 2 (June 2007), Article 13, 14 pages.

Digital Library

[8]

Michael R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman 8 Co., New York, NY.

Digital Library

[9]

R. Kleinberg. 2007. Geographic routing using hyperbolic space. In Proceedings of the 26th IEEE International Conference on Computer Communications (IEEE INFOCOM’07). 1902--1909.

Digital Library

[10]

Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, and Marián Boguñá. 2010. Hyperbolic geometry of complex networks. Physical Review E 82, 3 (2010), 036106.

[11]

Fragkiskos Papadopoulos, Rodrigo Aldecoa, and Dmitri Krioukov. 2015. Network geometry inference using common neighbors. Physical Review E 92, 2 (2015), 022807.

[12]

F. Papadopoulos, C. Psomas, and D. Krioukov. 2015. Network mapping by replaying hyperbolic growth. IEEE/ACM Transactions on Networking 23, 1 (Feb. 2015), 198--211.

Digital Library

[13]

Roldan Pozo. (n.d.). NGraph: A Simple (Network) Graph Library in C++. Retrieved February 21, 2020 from http://math.nist.gov/∼RPozo/ngraph/ngraph_index.html.

[14]

Ryan A. Rossi and Nesreen K. Ahmed. 2015. The network data repository with interactive graph analytics and visualization. In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI’15). 4292--4293. http://networkrepository.com.

[15]

Rik Sarkar. 2012. Low distortion Delaunay embedding of trees in hyperbolic plane. In Graph Drawing. Berlin, Germany, 355--366.

[16]

O. Tange. 2011. GNU parallel—The command-line power tool. ;login: The USENIX Magazine 36, 1 (Feb. 2011), 42--47.

Cited By

Pan YLyu N(2024)Hyperbolic-Embedding-Aided Geographic Routing in Intelligent Vehicular NetworksElectronics10.3390/electronics1303066113:3(661)Online publication date: 5-Feb-2024
https://doi.org/10.3390/electronics13030661
van der Kolk JSerrano MBoguñá M(2024)Random graphs and real networks with weak geometric couplingPhysical Review Research10.1103/PhysRevResearch.6.0133376:1Online publication date: 29-Mar-2024
https://doi.org/10.1103/PhysRevResearch.6.013337
Jeong DGunby-Mann ACohen SKatzmann MPham CBhakta AFriedrich TChin P(2024)Deep Distance Sensitivity OraclesComplex Networks & Their Applications XII10.1007/978-3-031-53468-3_38(452-463)Online publication date: 20-Feb-2024
https://doi.org/10.1007/978-3-031-53468-3_38
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Hyperbolic Embeddings for Near-Optimal Greedy Routing

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Published In

cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 25, Issue

Special Issue ALENEX 2018 and Regular Papers

2020

313 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/3388470

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 March 2020

Accepted: 01 January 2020

Revised: 01 November 2019

Received: 01 August 2018

Published in JEA Volume 25

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Cited By

Pan YLyu N(2024)Hyperbolic-Embedding-Aided Geographic Routing in Intelligent Vehicular NetworksElectronics10.3390/electronics1303066113:3(661)Online publication date: 5-Feb-2024
https://doi.org/10.3390/electronics13030661
van der Kolk JSerrano MBoguñá M(2024)Random graphs and real networks with weak geometric couplingPhysical Review Research10.1103/PhysRevResearch.6.0133376:1Online publication date: 29-Mar-2024
https://doi.org/10.1103/PhysRevResearch.6.013337
Jeong DGunby-Mann ACohen SKatzmann MPham CBhakta AFriedrich TChin P(2024)Deep Distance Sensitivity OraclesComplex Networks & Their Applications XII10.1007/978-3-031-53468-3_38(452-463)Online publication date: 20-Feb-2024
https://doi.org/10.1007/978-3-031-53468-3_38
Jankowski RAllard ABoguñá MSerrano M(2023)The D-Mercator method for the multidimensional hyperbolic embedding of real networksNature Communications10.1038/s41467-023-43337-514:1Online publication date: 21-Nov-2023
https://doi.org/10.1038/s41467-023-43337-5
Wang QJiang HJiang YYi SLi LXing CHuang J(2022)On Searching Multiple Disjoint Shortest Paths in Scale-Free Networks With Hyperbolic GeometryIEEE Transactions on Network Science and Engineering10.1109/TNSE.2022.31696919:4(2772-2785)Online publication date: 1-Jul-2022
https://doi.org/10.1109/TNSE.2022.3169691
Yang WQin YLi R(2022)A Network-Embedding-Based Approach for Scalable Network Navigability in Content-Centric Social IoTIEEE Internet of Things Journal10.1109/JIOT.2022.31514889:17(16418-16428)Online publication date: 1-Sep-2022
https://doi.org/10.1109/JIOT.2022.3151488
Diel RMitsche D(2021)On the largest component of subcritical random hyperbolic graphsElectronic Communications in Probability10.1214/21-ECP38026:noneOnline publication date: 1-Jan-2021
https://doi.org/10.1214/21-ECP380
Eppstein D(2021)Limitations on Realistic Hyperbolic Graph DrawingGraph Drawing and Network Visualization10.1007/978-3-030-92931-2_25(343-357)Online publication date: 23-Dec-2021
https://doi.org/10.1007/978-3-030-92931-2_25

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