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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1270–1276 | Cite as

A Method of Improving Initial Partition of Fiduccia–Mattheyses Algorithm

  • M. V. SheblaevEmail author
  • A. S. Sheblaeva
Part 1. Special issue “High Performance Data Intensive Computing” Editors: V. V. Voevodin, A. S. Simonov, and A. V. Lapin

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.

Keywords and phrases

balanced graph partitioning Fiduccia–Mattheyses algorithm FM algorithm min-cut balanced cut 

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References

  1. 1.
    M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness (W. H. Freeman, New York, 1979).zbMATHGoogle Scholar
  2. 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. 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. 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. 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. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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. 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.zbMATHGoogle Scholar
  9. 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.MathSciNetzbMATHGoogle Scholar
  10. 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.MathSciNetzbMATHGoogle Scholar
  11. 11.
    C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Courier, 1998).zbMATHGoogle Scholar
  12. 12.

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Space ResearchLomonosov Moscow State UniversityMoscowRussia
  2. 2.MSECLomonosov Moscow State UniversityMoscowRussia

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