Skip to main content
Log in

A Method of Improving Initial Partition of Fiduccia–Mattheyses Algorithm

  • Part 1. Special issue “High Performance Data Intensive Computing” Editors: V. V. Voevodin, A. S. Simonov, and A. V. Lapin
  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

This article presents a new method for finding initial partitioning for Fiduccia–Mattheyses algorithm that makes it possible to work out a qualitative approximate solution for the original balanced hypergraph partitioning problem. The proposed method uses geometrical properties and dimension reduction methods for metric spaces of large dimensions.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness (W. H. Freeman, New York, 1979).

    MATH  Google Scholar 

  2. R. Andersen et al., “Local graph partitioning using PageRank vectors,” in Proceedings of 47th Annual IEEE Symposium on Foundations of Computer Science, 2006, pp. 475–486. https://doi.org/ieeexplore.ieee.org/abstract/document/4031383/.

    Google Scholar 

  3. C. M. Fiduccia and R. M. Mattheyses, “A linear-time heuristic for improving network partitions,” in Proceedings of 19th Design Automation Conference (IEEE, 1982), pp. 175–181. https://doi.org/ieeexplore.ieee.org/document/1585498/.

    Google Scholar 

  4. J. Kim et al., “Genetic approaches for graph partitioning: a survey,” in Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation (ACM, 2011), pp. 473–480. https://doi.org/dl.acm.org/citation.cfm?id=2001642.

    Google Scholar 

  5. L. Lung-Tien et al., “A gradient method on the initial partition of Fiduccia–Mattheyses algorithm,” in Proceedings of the 1995 IEEE/ACM International Conference on Computer-Aided Design (IEEE, 1995), pp. 229–234. https://doi.org/ieeexplore.ieee.org/document/480017/.

    Google Scholar 

  6. C. Walshaw, “Multilevel refinement for combinatorial optimisation problems,” Ann. Operat. Res. 131, 325–372 (2004). https://doi.org/link.springer.com/article/10.1023/B:ANOR.0000039525.80601.15.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. S. Rusakov and M. V. Sheblaev, “Optimization of a partitioning algorithm for a hypergraph with arbitrary weights of vertices,” Vychisl. Metody Programm. 15, 400–410 (2014). https://doi.org/nummeth.srcc.msu.ru/zhurnal/tom_2014/pdf/v15r135.pdf.

    Google Scholar 

  8. L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res. 9, 2579–2605 (2008). https://doi.org/www.jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf.

    MATH  Google Scholar 

  9. L. van der Maaten, “Accelerating t-SNE using Tree-Based Algorithms,” J. Mach. Learn. Res. 15, 1–21 (2014). https://doi.org/jmlr.org/papers/volume15/vandermaaten14a/vandermaaten14a.pdf.

    MathSciNet  MATH  Google Scholar 

  10. F. Pedregosa et al., “Scikit-learn: machine learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011); https://doi.org/www.jmlr.org/papers/volume12/pedregosa11a/pedregosa11a.pdf.

    MathSciNet  MATH  Google Scholar 

  11. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Courier, 1998).

    MATH  Google Scholar 

  12. SuiteSparseMatrix Collection. https://doi.org/www.cise.ufl.edu/research/sparse/matrices/.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. V. Sheblaev.

Additional information

(Submitted by A. V. Lapin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheblaev, M.V., Sheblaeva, A.S. A Method of Improving Initial Partition of Fiduccia–Mattheyses Algorithm. Lobachevskii J Math 39, 1270–1276 (2018). https://doi.org/10.1134/S1995080218090196

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080218090196

Keywords and phrases

Navigation