Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Predictive Partitioning for Efficient BFS Traversal in Social Networks

  • Chapter
  • First Online:
Complex Networks VII

Part of the book series: Studies in Computational Intelligence ((SCI,volume 644))

Abstract

In this paper we show how graph structure can be used to significantly reduce the computational bottleneck of the Breadth First Search algorithm (the foundation of many graph traversal techniques) for social networks. In particular, we address parallel implementations where the bottleneck is the number of messages between processors emitted at the peak iteration. First, we derive an expression for the expected degree distribution of vertices in the frontier of the algorithm which is shown to be highly skewed. Subsequently, we derive an expression for the expected message along an edge in a particular iteration. This skew suggests a weighted, iteration based, partition would be advantageous. Empirical simulations show that such partitions can reduce the message overhead in the order of 20 % for graphs with common social network structural properties. These results have implications for graph processing in multiprocessor and distributed computing environments.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A good estimate of the number of vertices expected in each iteration of BFS can be obtained from a single graph traversals.

  2. 2.

    Here we use the YouTube friendship graph as an example: the power law exponent = \(-2\) and \(t_\tau \) = \(\{0.0006,0.02,0.19,0.53,0.81,0.93,0.97,0.99,1\}\), the results are similar for the other graphs we examined.

  3. 3.

    https://sites.google.com/site/structuralgraphproperties/home.

  4. 4.

    http://konect.uni-koblenz.de.

  5. 5.

    Alternatively one could insert a concentrated degree distribution for \(p_k\) in (4) and see that \(\pi _{k}^{tau} = p_k\).

References

  1. Merrill, D., Garland, M., Grimshaw, A.: Scalable GPU graph traversal. In: 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, vol. 47, no. 8, pp. 117–128, Feb 2012

    Google Scholar 

  2. Buluç, A., Madduri, K.: Graph partitioning for scalable distributed graph computations. Contemp. Math. 588, 83 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Krzywdzinski, K., Kowalski, D.: On the complexity of distributed BFS in ad hoc networks with spontaneous wake-up. Discrete Math. Theor. Comput. Sci. 15(3), 101–118 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Shang, H., Kitsuregawa, M.: Efficient breadth-first search on large graphs with skewed degree distributions. In: Joint 2013 EDBT/ICDT Conferences, EDBT’13 Proceedings, Genoa, Italy, March 18–22, 2013, pp. 311–322 (2013)

    Google Scholar 

  5. Chen, R., Shi, J., Chen, Y., Chen, H.: PowerLyra: differentiated graph computation and partitioning on skewed graphs. In: Proceedings of the Tenth European Conference on Computer Systems, EuroSys’15, pp. 1:1–1:15. ACM, New York, NY, USA (2015)

    Google Scholar 

  6. Fu, Z., Dasari, H., Berzins, M., Thompson, B.: Parallel breadth first search on GPU clusters. SCI Institute, University of Utah, SCI Technical report UUSCI-2014-002 (2014)

    Google Scholar 

  7. Wang, Y., Owens, J.D.: Large-scale graph processing algorithms on the GPU. UC Davis, Technical report (2013)

    Google Scholar 

  8. Buluç, A., Beamer, S., Madduri, K., Asanović, K., Patterson, D.: Distributed-memory breadth-first search on massive graphs. In: Bader, D. (ed.) Parallel Graph Algorithms. CRC Press, Taylor-Francis (2016). https://www.crcpress.com/Parallel-Graph-Algorithms/Bader/9781466573260

  9. Luo, L., Wong, M., Hwu, W.-M.: An effective GPU implementation of breadth-first search. Proceedings of the 47th Design Automation Conference. DAC’10, pp. 52–55. ACM, New York, NY, USA (2010)

    Google Scholar 

  10. Bisson, M., Bernaschi, M., Mastrostefano, E.: Parallel distributed breadth first search on the Kepler architecture (2014). arXiv:1408.1605

  11. Buluç, A., Madduri, K.: Parallel breadth-first search on distributed memory systems. In: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC’11, pp. 65:1–65:12. ACM, New York, NY, USA (2011)

    Google Scholar 

  12. Yuan, L., Ding, C., Tefankovic, D., Zhang, Y.: Modeling the locality in graph traversals. In: ICPP. IEEE Computer Society, pp. 138–147 (2012)

    Google Scholar 

  13. Buluç, A., Meyerhenke, H., Safro, I., Sanders, P., Schulz, C.: Recent advances in graph partitioning (2013). arXiv:1311.3144

  14. Akiba, T., Iwata, Y., Yoshida, Y.: Fast exact shortest-path distance queries on large networks by pruned landmark labeling. In: Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, SIGMOD’13, pp. 349–360. ACM, New York, NY, USA (2013). http://doi.acm.org/10.1145/2463676.2465315

    Google Scholar 

  15. Idwan, S., Etaiwi, W.: Computing breadth first search in large graph using hmetis partitioning. Eur. J. Sci. Res. 29(2), 215–221 (2009)

    Google Scholar 

  16. Abou-Rjeili, A., Karypis, G.: Multilevel algorithms for partitioning power-law graphs. Proceedings of the 20th International Conference on Parallel and Distributed Processing. IPDPS’06, pp. 124–124. IEEE Computer Society, Washington, DC, USA (2006)

    Google Scholar 

  17. Hong, S., Kim, S.K., Oguntebi, T., Olukotun, K.: Accelerating CUDA graph algorithms at maximum warp. SIGPLAN Not. 46(8), 267–276 (2011)

    Article  Google Scholar 

  18. Then, M., Kaufmann, M., Chirigati, F., Hoang-Vu, T.-A., Pham, K., Kemper, A., Neumann, T., Vo, H.T.: The more the merrier: Efficient multi-source graph traversal. In: Proceedings of VLDB Endow., vol. 8, no. 4, pp. 449–460 (2014). http://dx.doi.org/10.14778/2735496.2735507

    Google Scholar 

  19. Karypis, G., Kumar, V.: Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48, 96–129 (1998)

    Article  MATH  Google Scholar 

  20. Kurant, M., Markopoulou, A., Thiran, P.: On the bias of BFS (breadth first search). In: 22nd International Teletraffic Congress (ITC), pp. 1–8 (2010)

    Google Scholar 

  21. Mahadevan, P., Hubble, C., Krioukov, D., Huffaker, B., Vahdat, A.: Orbis: rescaling degree correlations to generate annotated Internet topologies. SIGCOMM Comput. Commun. Rev. 37(4), 325–336 (2007)

    Article  Google Scholar 

  22. Achlioptas, D., Clauset, A., Kempe, D., Moore, C.: On the bias of traceroute sampling: or, power-law degree distributions in regular graphs. In: STOC’05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, May 2005, pp. 694–703

    Google Scholar 

  23. Fay, D., Haddadi, H., Uhlig, S., Kilmartin, L., Moore, A.W., Kunegis, J., Iliofotou, M.: Discriminating graphs through spectral projections. Comput. Netw. 55(15), 3458–3468 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing, Bournemouth University, Poole, UK

    Damien Fay

Authors
  1. Damien Fay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Damien Fay .

Editor information

Editors and Affiliations

  1. LE2I , UFR Sciences et Techniques, Université de Bourgogne, Dijon, France

    Hocine Cherifi

  2. New York University, Center for Data Science, New York, USA

    Bruno Gonçalves

  3. BioComplex Laboratory, Computer Sciences, Florida Institute of Technology, Melbourne, FL, Florida, USA

    Ronaldo Menezes

  4. 111 Dana, Physics Department, Northeastern University, Boston, Massachusetts, USA

    Roberta Sinatra

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Fay, D. (2016). Predictive Partitioning for Efficient BFS Traversal in Social Networks. In: Cherifi, H., Gonçalves, B., Menezes, R., Sinatra, R. (eds) Complex Networks VII. Studies in Computational Intelligence, vol 644. Springer, Cham. https://doi.org/10.1007/978-3-319-30569-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30569-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30568-4

  • Online ISBN: 978-3-319-30569-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation