Skip to main content
SpringerLink
Log in
Book cover

European Symposium on Algorithms

ESA 2009: Algorithms - ESA 2009 pp 566–577Cite as

Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5757))

Abstract

In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(n k 2 3k) time and the problem to count the number of perfect matchings in O  ∗ (2k) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ,σ]-domination problems with finite or cofinite ρ and σ on tree decompositions. These include many well known graph problems. We give additional results on many more graph covering and partitioning problems.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alber, J., Bodlaender, H.L., Fernau, H., Kloks, T., Niedermeier, R.: Fixed parameter algorithms for dominating set and related problems on planar graphs. Algorithmica 33, 461–493 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alber, J., Niedermeier, R.: Improved tree decomposition based algorithms for domination-like problems. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 613–627. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Fourier meets Möbius: Fast subset convolution. In: Proceedings of the 39th Annual Symposium on Theory of Computing, STOC 2007, pp. 67–74 (2007)

    Google Scholar 

  4. Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25, 1305–1317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comp. Sc. 209, 1–45 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. The Computer Journal 51(3), 255–269 (2008)

    Article  Google Scholar 

  7. Bodlaender, H.L., Koster, A.M.C.A.: Treewidth computations I. upper bounds. Technical Report UU-CS-2008-032, Department of Information and Computing Sciences, Utrecht University, Utrecht, the Netherlands, Submitted (2008)

    Google Scholar 

  8. Bodlaender, H.L., van Antwerpen-de Fluiter, B.: Reduction algorithms for graphs of small treewidth. Information and Computation 167, 86–119 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dorn, F.: Dynamic programming and fast matrix multiplication. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 280–291. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Dorn, F.: How to use planarity efficiently: New tree-decomposition based algorithms. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 280–291. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Dorn, F., Fomin, F.V., Thilikos, D.M.: Catalan structures and dynamic programming in h-minor-free graphs. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, pp. 631–640 (2008)

    Google Scholar 

  12. Dorn, F., Penninkx, E., Bodlaender, H.L., Fomin, F.V.: Efficient exact algorithms on planar graphs: Exploiting sphere cut branch decompositions. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 95–106. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Fürer, M.: Faster integer multiplication. In: Proceedings of the 39th Annual Symposium on Theory of Computing, STOC 2007 (2007)

    Google Scholar 

  14. Kloks, T.: Treewidth. Computations and Approximations. LNCS, vol. 842. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  15. Telle, J.A.: Complexity of domination-type problems in graphs. Nordic J. Comput. 1, 157–171 (1994)

    MathSciNet  Google Scholar 

  16. Telle, J.A., Proskurowski, A.: Algorithms for vertex partitioning problems on partial k-trees. SIAM J. Disc. Math. 10, 529–550 (1997)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, P.O.Box 80.089, 3508 TB, Utrecht, The Netherlands

    Johan M. M. van Rooij & Hans L. Bodlaender

  2. Computer Science Department, RWTH Aachen University, 52056, Aachen, Germany

    Peter Rossmanith

Authors
  1. Johan M. M. van Rooij
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans L. Bodlaender
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Rossmanith
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amos Fiat

  2. Fakultät für Informatik, Universität Karlsruhe (TH), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter Sanders

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Rooij, J.M.M., Bodlaender, H.L., Rossmanith, P. (2009). Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_51

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04128-0_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation