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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 author. Email: sanders@kit.edu
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Abstract

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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

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