Skip to main content

Empirical Evaluation of Graph Partitioning Using Spectral Embeddings and Flow

  • Conference paper
Experimental Algorithms (SEA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5526))

Included in the following conference series:

Abstract

We present initial results from the first empirical evaluation of a graph partitioning algorithm inspired by the Arora-Rao-Vazirani algorithm of [5], which combines spectral and flow methods in a novel way. We have studied the parameter space of this new algorithm, e.g., examining the extent to which different parameter settings interpolate between a more spectral and a more flow-based approach, and we have compared results of this algorithm to results from previously known and optimized algorithms such as Metis.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Milman, V.: λ 1, isoperimetric inequalities for graphs and superconcentrators. J. Combin. Theory B 38, 73–88 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andersen, R., Lang, K.: An algorithm for improving graph partitions. In: SODA 2008: Proceedings of the 19th ACM-SIAM Symposium on Discrete Algorithms, pp. 651–660 (2008)

    Google Scholar 

  3. Arora, S., Hazan, E., Kale, S.: \({O}(\sqrt {\log n)}\) approximation to sparsest cut in \(\tilde{O}(n^2)\) time. In: FOCS 2004: Proceedings of the 45th Annual Symposium on Foundations of Computer Science, pp. 238–247 (2004)

    Google Scholar 

  4. Arora, S., Kale, S.: A combinatorial, primal-dual approach to semidefinite programs. In: STOC 2007: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 227–236 (2007)

    Google Scholar 

  5. Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. In: STOC 2004: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 222–231 (2004)

    Google Scholar 

  6. Arora, S., Rao, S., Vazirani, U.: Geometry, flows, and graph-partitioning algorithms. Communications of the ACM 51(10), 96–105 (2008)

    Article  Google Scholar 

  7. Cherkassky, B., Goldberg, A., Martin, P., Setubal, J., Stolfi, J.: Augment or push: a computational study of bipartite matching and unit-capacity flow algorithms. Journal of Experimental Algorithmics 3, Article 8 (1998)

    Google Scholar 

  8. Cherkassky, B., Goldberg, A.V.: On implementing push-relabel method for the maximum flow problem. Algorithmica 19, 390–410 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chung, F.: Spectral graph theory. CBMS Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence (1997)

    MATH  Google Scholar 

  10. Goldberg, A., Rao, S.: Beyond the flow decomposition barrier. Journal of the ACM 45, 783–797 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Guattery, S., Miller, G.: On the quality of spectral separators. SIAM Journal on Matrix Analysis and Applications 19, 701–719 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20, 359–392 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Khandekar, R., Rao, S., Vazirani, U.: Graph partitioning using single commodity flows. In: STOC 2006: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 385–390 (2006)

    Google Scholar 

  14. Lang, K., Rao, S.: Finding near-optimal cuts: an empirical evaluation. In: SODA 1993: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 212–221 (1993)

    Google Scholar 

  15. Leighton, T., Rao, S.: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM 46(6), 787–832 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Orecchia, L., Schulman, L., Vazirani, U., Vishnoi, N.: On partitioning graphs via single commodity flows. In: STOC 2008: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 461–470 (2008)

    Google Scholar 

  17. Walshaw, C., Cross, M.: Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM Journal on Scientific Computing 22(1), 63–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lang, K.J., Mahoney, M.W., Orecchia, L. (2009). Empirical Evaluation of Graph Partitioning Using Spectral Embeddings and Flow. In: Vahrenhold, J. (eds) Experimental Algorithms. SEA 2009. Lecture Notes in Computer Science, vol 5526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02011-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02011-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02010-0

  • Online ISBN: 978-3-642-02011-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics