Skip to main content
SpringerLink
Log in

A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators

  • Conference paper
  • First Online:
Learning and Intelligent Optimization (LION 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8426))

Included in the following conference series:

  • 1100 Accesses

Abstract

The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size. Recently, Hager and Hungerford [1] developed a continuous bilinear programming formulation of the VSP. In this paper, we reinforce the bilinear programming approach with a multilevel scheme for learning the structure of the graph.

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. Hager, W.W., Hungerford, J.T.: Continuous quadratic programming formulations of optimization problems on graphs. European J. Oper. Res. (2013). http://dx.doi.org/10.1016/j.ejor.2014.05.042

  2. Balas, E., de Souza, C.C.: The vertex separator problem: a polyhedral investigation. Math. Program. 103, 583–608 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Pothen, A., Simon, H.D., Liou, K.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11(3), 430–452 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ullman, J.: Computational Aspects of VLSI. Computer Science Press, Rockville (1984)

    MATH  Google Scholar 

  5. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49, 291–307 (1970)

    Article  MATH  Google Scholar 

  6. Bui, T., Jones, C.: Finding good approximate vertex and edge partitions is NP-hard. Inf. Process. Lett. 42, 153–159 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. In: Proceedings of the 19th Design Automation Conference Las Vegas, NV, pp. 175–181 (1982)

    Google Scholar 

  8. Feige, U., Hajiaghayi, M., Lee, J.: Improved approximation algorithms for vertex separators. SIAM J. Comput. 38, 629–657 (2008)

    Article  MathSciNet  Google Scholar 

  9. Ron, D., Safro, I., Brandt, A.: Relaxation-based coarsening and multiscale graph organization. Multiscale Model. Simul. 9(1), 407–423 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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

  11. Leiserson, C., Lewis, J.: Orderings for parallel sparse symmetric factorization. In: Third SIAM Conference on Parallel Processing for Scientific Computing, pp. 27–31 (1987)

    Google Scholar 

  12. Safro, I., Ron, D., Brandt, A.: A multilevel algorithm for the minimum 2-sum problem. J. Graph Algorithms Appl. 10, 237–258 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dezső, B., Jüttner, A., Kovács, P.: Lemon - an open source C++ graph template library. Electron. Notes Theoret. Comput. Sci. 264(5), 23–45 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, USA

    William W. Hager & James T. Hungerford

  2. School of Computing, Clemson University, Clemson, SC, USA

    Ilya Safro

Authors
  1. William W. Hager
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James T. Hungerford
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ilya Safro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James T. Hungerford .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. AT&T Labs Research, Middletown, New Jersey, USA

    Mauricio G.C. Resende

  3. University of Florida, Gainesville, Florida, USA

    Chrysafis Vogiatzis

  4. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Jose L. Walteros

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Hager, W.W., Hungerford, J.T., Safro, I. (2014). A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators. In: Pardalos, P., Resende, M., Vogiatzis, C., Walteros, J. (eds) Learning and Intelligent Optimization. LION 2014. Lecture Notes in Computer Science(), vol 8426. Springer, Cham. https://doi.org/10.1007/978-3-319-09584-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09584-4_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09583-7

  • Online ISBN: 978-3-319-09584-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation