Skip to main content Accessibility help
×
Home
Hostname: page-component-564cf476b6-zvgck Total loading time: 0.273 Render date: 2021-06-19T10:45:51.040Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Linear work generation of R-MAT graphs

Published online by Cambridge University Press:  29 May 2020

Lorenz Hübschle-Schneider
Affiliation:
Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany (e-mail: huebschle@kit.edu)
Peter Sanders
Affiliation:
Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany (e-mail: huebschle@kit.edu)
Corresponding
Rights & Permissions[Opens in a new window]

Abstract

R-MAT (for Recursive MATrix) is a simple, widely used model for generating graphs with a power law degree distribution, a small diameter, and communitys structure. It is particularly attractive for generating very large graphs because edges can be generated independently by an arbitrary number of processors. However, current R-MAT generators need time logarithmic in the number of nodes for generating an edge— constant time for generating one bit at a time for node IDs of the connected nodes. We achieve constant time per edge by precomputing pieces of node IDs of logarithmic length. Using an alias table data structure, these pieces can then be sampled in constant time. This simple technique leads to practical improvements by an order of magnitude. This further pushes the limits of attainable graph size and makes generation overhead negligible in most situations.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

Action Editor: Ulrik Brandes

References

Barabasi, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509512.CrossRefGoogle ScholarPubMed
Bläsius, T., Friedrich, T., Katzmann, M., Meyer, U., Penschuck, M., & Weyand, C. (2019). Efficiently generating geometric inhomogeneous and hyperbolic random graphs. In 27th European symposium on algorithms (ESA) (pp. 21:1–21:14).Google Scholar
Chakrabarti, D., Zhan, Y., & Faloutsos, C. (2004). R-MAT: A recursive model for graph mining. In SIAM conference on data mining (SDM) (pp. 442446). SIAM.CrossRefGoogle Scholar
Drobyshevskiy, M., & Turdakov, D. (2020). Random graph modeling. ACM Computing Surveys, 52(6), 131:1–131:36.Google Scholar
Funke, D., Lamm, S., Meyer, U., Penschuck, M., Sanders, P., Schulz, C., …, von Looz, M. (2019). Communication-free massively distributed graph generation. Journal of Parallel and Distributed Computing, 131, 200217.CrossRefGoogle Scholar
Goldenberg, A., Zheng, A. X, Fienberg, S. E., & Airoldi, E. M. (2010). A survey of statistical network models. Foundations and Trends in Machine Learning, 2(2), 129233.CrossRefGoogle Scholar
Hübschle-Schneider, L., & Sanders, P. (2019a). Linear work generation of R-MAT graphs. arXiv/CoRR,arXiv:1905.03525.CrossRefGoogle Scholar
Hübschle-Schneider, L., & Sanders, P. (2019b). Parallel weighted random sampling. In 27th European symposium on algorithms (ESA) (pp. 59:1–59:24). LIPIcs.Google Scholar
Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., & Boguná, M. (2010). Hyperbolic geometry of complex networks. Physical Review E, 82(3), 036106-1-036106-18.CrossRefGoogle ScholarPubMed
Lancichinetti, A., Fortunato, S., & Radicchi, F. (2008). Benchmark graphs for testing community detection algorithms. Physical Review E, 78(4), 046110.CrossRefGoogle ScholarPubMed
Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., & Ghahramani, Z. (2010). Kronecker graphs: An approach to modeling networks. Journal of Machine Learning Research, 11, 9851042.Google Scholar
Leskovec, J., & Faloutsos, C. (2007). Scalable modeling of real graphs using Kronecker multiplication. In 24th international conference on machine learning (ICML) (pp. 497504). ACM.CrossRefGoogle Scholar
Mahdian, M., & Xu, Y. (2007). Stochastic kronecker graphs. In 5th international workshop on algorithms and models for the web-graph (WAW) (pp. 179186). Springer.CrossRefGoogle Scholar
Moreno, S., Pfeiffer, J. J., & Neville, J. (2018). Scalable and exact sampling method for probabilistic generative graph models. Data Mining and Knowledge Discovery, 32(6), 15611596.CrossRefGoogle Scholar
Murphy, R. C., Wheeler, K. B., Barrett, B. W., & Ang, J. A. (2010). Introducing the Graph 500. Cray user’s group.Google Scholar
Penschuck, M., Brandes, U., Hamann, M., Lamm, S., Meyer, U., Safro, I., …, Schulz , C. (2020). Recent advances in scalable network generation. arXiv/CoRR,arXiv:2003.00736.Google Scholar
Sanders, P., & Schulz, C. (2016). Scalable generation of scale-free graphs. Information Processing Letters, 116(7), 489491.CrossRefGoogle Scholar
Staudt, C. L., Sazonovs, A., & Meyerhenke, H. (2016). NetworKit: A tool suite for large-scale complex network analysis. Network Science, 4(4), 508530.CrossRefGoogle Scholar
Vose, M. D. (1991). A linear algorithm for generating random numbers with a given distribution. IEEE Transactions on Software Engineering (TSE), 17(9), 972975.CrossRefGoogle Scholar
Walker, A. J. (1977). An efficient method for generating discrete random variables with general distributions. ACM Transactions on Mathematical Software (TOMS), 3(3), 253256.CrossRefGoogle Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393(6684), 440.CrossRefGoogle ScholarPubMed
You have Access
Open access
1
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Linear work generation of R-MAT graphs
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Linear work generation of R-MAT graphs
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Linear work generation of R-MAT graphs
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *