Skip to main content
SpringerLink
Log in

Optimal Solutions for Frequency Assignment Problems via Tree Decomposition

  • Conference paper
Graph-Theoretic Concepts in Computer Science (WG 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

Included in the following conference series:

Abstract

In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small and medium-sized real-life instances of the frequency assignment problem to optimality. Moreover, with an iterative version of the algorithm we obtain good lower bounds for large-sized instances within reasonable time and memory limits.

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 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. S. Arnborg, D.G. Corneil, and A. Proskurowski. Complexity of finding embeddins in a k-tree. SIAM Journal on Algebraic and Discrete Methods, 8:277–284, 1987. 341

    Article  MATH  MathSciNet  Google Scholar 

  2. H.L. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11(1-2):1–21, 1993. 339

    MATH  MathSciNet  Google Scholar 

  3. H.L. Bodlaender. “A linear time algorithm for finding tree-decompositions of small treewidth”. SIAM Journal on Computing, 25(6):1305–1317, 1996. 341

    Article  MATH  MathSciNet  Google Scholar 

  4. D.J. Castelino, S. Hurley, and N.M. Stephens. A tabu search algorithm for frequency assignment. Annals of Operations Research, 63:301–319, 1996. 339

    Article  MATH  Google Scholar 

  5. A. Kolen. A genetic algorithm for frequency assignment. Technical report, Maastricht University, 1999. Available at http://www.unimaas.nl/~akolen/. 339, 347

  6. A.M.C.A. Koster, C.P.M. van Hoesel, and A.W.J. Kolen. The partial constraint satisfaction problem: Facets and lifting theorems. Operations Research Letters, 23(3-5):89–97, 1998. 339, 341

    Article  MATH  MathSciNet  Google Scholar 

  7. A.M.C.A. Koster, C.P.M. van Hoesel, and A.W.J. Kolen. Solving frequency assignment problems via tree-decomposition. Technical Report RM 99/011, Maastricht University, 1999. Available at http://www.unimaas.nl/~akoster/. 340, 341, 343, 346

  8. N. Robertson and P.D. Seymour. Graph minors. II. algorithmic aspects of treewidth. Journal of Algorithms, 7:309–322, 1986. 339, 341

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Tiourine, C. Hurkens, and J.K. Lenstra. “An overview of algorithmic approaches to frequency assignment problems”. In Calma Symposium on Combinatorial Algorithms for Military Applications, pages 53–62, 1995. Available at http://www.win.tue.nl/math/bs/combopt/hurkens/calma.html. 339

  10. S. R. Tiourine, C.A.J. Hurkens, and J.K. Lenstra. Local search algorithms for the radio link frequency assignment problem. Telecommunication systems, to appear, 1999. 339, 339

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200, MD Maastricht, The Netherlands

    Arie M. C. A. Koster, Stan P.M. van Hoesel & Antoon W.J. Kolen

Authors
  1. Arie M. C. A. Koster
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stan P.M. van Hoesel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antoon W.J. Kolen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koster, A.M.C.A., van Hoesel, S.P., Kolen, A.W. (1999). Optimal Solutions for Frequency Assignment Problems via Tree Decomposition. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-46784-X_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation