Skip to main content
SpringerLink
Log in

Distributed Algorithms for Finding Local Clusters Using Heat Kernel Pagerank

  • Conference paper
  • First Online:
Algorithms and Models for the Web Graph (WAW 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9479))

Included in the following conference series:

Abstract

We consider the problem of computing local clusters in large graphs distributed across nodes in a network using two different models of distributed computation. We give a distributed algorithm that computes a local cluster in time that depends only logarithmically on the size of the graph in the CONGEST model. In particular, when the conductance of the optimal local cluster is known, the algorithm runs in time entirely independent of the size of the graph and depends only on error bounds for approximation. We also show that the local cluster problem can be computed in the k-machine distributed model in sublinear time. The speedup of our local cluster algorithms is mainly due to the use of our distributed algorithm for heat kernel pagerank.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Andersen, R., Chung, F., Lang, K.: Local graph partitioning using pagerank vectors. In: FOCS, pp. 475–486. IEEE (2006)

    Google Scholar 

  2. Andersen, R., Peres, Y.: Finding sparse cuts locally using evolving sets. In: STOC, pp. 235–244. ACM (2009)

    Google Scholar 

  3. Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. JACM 56(2), 1–37 (2009). Article no. 5

    Article  MathSciNet  Google Scholar 

  4. Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1), 107–117 (1998)

    Article  Google Scholar 

  5. Chung, F.: Spectral Graph Theory. American Mathematical Society, Providence (1997)

    MATH  Google Scholar 

  6. Chung, F., Simpson, O.: Computing heat kernel pagerank and a local clustering algorithm. In: Jan, K., Miller, M., Froncek, D. (eds.) IWOCA 2014. LNCS, vol. 8986, pp. 110–121. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  7. Chung, F., Simpson, O.: Computing heat kernel pagerank and a local clustering algorithm. arXiv preprint arXiv:1503.03155 (2015)

  8. Chung, F., Simpson, O.: Distributed algorithms for finding local clusters using heat kernel pagerank. arXiv preprint arXiv:1507.08967 (2015)

  9. Das Sarma, A., Molla, A.R., Pandurangan, G.: Distributed computation of sparse cuts via random walks. In: ICDCN, pp. 6:1–6:10 (2015)

    Google Scholar 

  10. Das Sarma, A., Molla, A.R., Pandurangan, G., Upfal, E.: Fast distributed pagerank computation. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds.) ICDCN 2013. LNCS, vol. 7730, pp. 11–26. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Das Sarma, A., Nanongkai, D., Pandurangan, G., Tetali, P.: Distributed random walks. JACM 60(1), 201–210 (2013). Article no. 2

    Google Scholar 

  12. Dean, J., Ghemawat, S.: Mapreduce: simplified data processing on large clusters. In: OSDI (2004)

    Google Scholar 

  13. Gharan, S.O., Trevisan, L.: Approximating the expansion profile and almost optimal local graph clustering. In: FOCS, pp. 187–196. IEEE (2012)

    Google Scholar 

  14. Klauck, H., Nanongkai, D., Pandurangan, G., Robinson, P.: Distributed computation of large-scale graph problems. In: SODA, pp. 391–410. SIAM (2015)

    Google Scholar 

  15. Kloster, K., Gleich, D.F.: Heat kernel based community detection. In: ACM SIGKDD, pp. 1386–1395. ACM (2014)

    Google Scholar 

  16. Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Statistical properties of community structure in large social and information networks. In: WWW, pp. 695–704. ACM (2008)

    Google Scholar 

  17. Liao, C.S., Lu, K., Baym, M., Singh, R., Berger, B.: Isorankn: spectral methods for global alignment of multiple protein networks. Bioinformatics 25(12), i253–i258 (2009)

    Article  Google Scholar 

  18. Lovász, L., Simonovits, M.: The mixing rate of markov chains, an isoperimetric inequality, and computing the volume. In: FOCS, pp. 346–354. IEEE (1990)

    Google Scholar 

  19. Lovász, L., Simonovits, M.: Random walks in a convex body and an improved volume algorithm. Random Struct. Algorithms 4(4), 359–412 (1993)

    Article  MATH  Google Scholar 

  20. Low, Y., Gonzalez, J., Kyrola, A., Bickson, D., Guestrin, C., Hellerstein, J.M.: Graphlab: a new framework for parallel machine learning. In: UAI, pp. 340–349 (2010)

    Google Scholar 

  21. Malewicz, G., Austern, M.H., Bik, A.J., Dehnert, J.C., Horn, I., Leiser, N., Czajkowski, G.: Pregel: a system for large-scale graph processing. In: SIGMOD International Conference on Management of data, pp. 135–146. ACM (2010)

    Google Scholar 

  22. Orecchia, L., Sachdeva, S., Vishnoi, N.K.: Approximating the exponential, the lanczos method and an \(\tilde{O}\)(m)-time spectral algorithm for balanced separator. In: STOC, pp. 1141–1160. ACM (2012)

    Google Scholar 

  23. Pandurangan, G., Khan, M.: Theory of communication networks. In: Atallah, M.J., Blanton, M. (eds.) Algorithms and Theory of Computation Handbook. Chapman & Hall/CRC, Boca Raton (2010)

    Google Scholar 

  24. Peleg, D.: Distributed computing. In: SIAM Monographs on Discrete Mathematics and Applications 5 (2000)

    Google Scholar 

  25. Spielman, D.A., Teng, S.H.: Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In: STOC, pp. 81–90. ACM (2004)

    Google Scholar 

Download references

Acknowledgements

The authors would like to warmly thank Yiannis Koutis for discussion and for suggesting the problem of finding efficient distributed algorithms, as well as the anonymous reviewers for their suggestions for improving the paper.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of California, San Diego, La Jolla, CA, 92093, USA

    Fan Chung & Olivia Simpson

Authors
  1. Fan Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olivia Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olivia Simpson .

Editor information

Editors and Affiliations

  1. Purdue University, West Lafayette, Indiana, USA

    David F. Gleich

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Júlia Komjáthy

  3. University of Twente, Enschede, The Netherlands

    Nelly Litvak

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Chung, F., Simpson, O. (2015). Distributed Algorithms for Finding Local Clusters Using Heat Kernel Pagerank. In: Gleich, D., Komjáthy, J., Litvak, N. (eds) Algorithms and Models for the Web Graph. WAW 2015. Lecture Notes in Computer Science(), vol 9479. Springer, Cham. https://doi.org/10.1007/978-3-319-26784-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26784-5_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26783-8

  • Online ISBN: 978-3-319-26784-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation