Skip to main content
Springer Nature Link
Log in

A Multi-scale Algorithm for the Linear Arrangement Problem

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

Included in the following conference series:

Abstract

Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a linear-time algorithm for this problem, based on the multi-scale paradigm. Experimental results are similar to those of the best known approaches, while the running time is significantly better, enabling it to deal with much larger graphs. The paper contains a general multi-scale construction, which may be used for a broader range of ordering problems.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. J. E. Atkins, E. G. Boman and B. Hendrickson, “A Spectral Algorithm for Seriation and the Consecutive Ones Problem”, SIAM Journal on Computing 28 (1998), 297–310.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. T. Barnard and H. D. Simon, “A Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems”, Concurrency: Practice & Experience 6 (1994), 101–117.

    Article  Google Scholar 

  3. J. Diaz, J. Petit and M. Serna, “A Survey on Graph Layout Problems”, Technical report LSI-00-61-R, Universitat Politècnica de Catalunya, Departament de Llenguatges i Sistemes Informàtics, 2000.

    Google Scholar 

  4. M. R. Garey and D. S. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness,W. H. Freeman, 1979.

    Google Scholar 

  5. D. Harel and Y. Koren, “AFast Multi-Scale Method for Drawing Graphs Nicely”, Proceedings of Graph Drawing’00, Lecture Notes in Computer Science, Vol. 1984, Springer Verlag, pp. 183–196, 2000.

    Google Scholar 

  6. M. Juvan and B. Mohar, “Optimal Linear Labelings and Eigenvalues of Graphs”, Discrete Applied Math. 36 (1992), 153–168.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Karypis and V. Kumar, “A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs”, SIAM Journal on Scientific Computing 20 (1999), 359–392.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Kirkpatrick J. Gelatt and M.P. Vecchi, “Optimization by Simulated Annealing”, Science 220 (1983), 671–680.

    Article  MathSciNet  Google Scholar 

  9. Y. Koren, L. Carmel and D. Harel “ACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs”, Technical Report MCS01-17, Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 2001. To appear in Proc. IEEE Information Visualization 2002.

    Google Scholar 

  10. Y. Koren and D. Harel “Multi-Scale Algorithm for the Linear Arrangement Problem”, Technical Report MCS02-04, Faculty of Mathematics and Computer Science, TheWeizmann Institute of Science, 2002.Available http://www.wisdom.weizmann.ac.il/reports.html

  11. J. Petit, “Experiments on the Minimum Linear Arrangement Problem”, Technical report LSI-01-7-R, Universitat Politècnica de Catalunya, Departament de Llenguatges i Sistemes Informàtics, 2001.

    Google Scholar 

  12. S. H. Teng, “Coarsening, Sampling, and Smoothing: Elements of the Multilevel Method”, Algorithms for Parallel Processing, IMA Volumes in Mathematics and its Applications, Vol. 105, Springer Verlag, pp. 247–276, 1999.

    MathSciNet  Google Scholar 

  13. C. Walshaw, “Multilevel Re.nement for Combinatorial Optimisation Problems”, Technical Report 01/IM/73, Comp. Math. Sci., Univ. Greenwich, London, UK, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Yehuda Koren & David Harel

Authors
  1. Yehuda Koren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Harel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koren, Y., Harel, D. (2002). A Multi-scale Algorithm for the Linear Arrangement Problem. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-36379-3_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics