Skip to main content
SpringerLink
Log in

Roman Domination: A Parameterized Perspective

  • Conference paper
SOFSEM 2006: Theory and Practice of Computer Science (SOFSEM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3831))

  • 857 Accesses

Abstract

We analyze Roman Domination from a parameterized perspective. More specifically, we prove that this problem is W[2]-complete for general graphs. However, parameterized algorithms are presented for graphs of bounded treewidth and for planar graphs. Moreover, it is shown that a parametric dual of Roman Domination is in \({\mathcal FPT}\).

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. Alber, J., Fan, H., Fellows, M.R., Fernau, H., Niedermeier, R., Rosamond, F., Stege, U.: Refined Search Tree Techniques for the Planar Dominating Set Problem. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 111–122. Springer, Heidelberg (2001); Long version to appear in Journal of Computer and System Sciences

    Chapter  Google Scholar 

  2. Benecke, S.: Higher Order Domination of Graphs. Master’s Thesis, Department of Applied Mathematics of the University of Stellebosch, South Africa (2004)

    Google Scholar 

  3. Bodlaender, H.L.: Dynamic Programming on Graphs with Bounded Treewidth. In: Lepistö, T., Salomaa, A. (eds.) ICALP 1988. LNCS, vol. 317, pp. 105–119. Springer, Heidelberg (1988)

    Google Scholar 

  4. Cesati, M.: The Turing Way to Parameterized Complexity. Journal of Computer and System Sciences 67, 654–685 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cesati, M., Di Ianni, M.: Computation Models for Parameterized Complexity. Mathematical Logic Quarterly 43, 179–202 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, Y., Flum, J.: Machine Characterization of the Classes of the W-Hierarchy. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 114–127. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Cockayne, E.J., Dreyer Jr., P.A., Hedetniemi, S.M., Hedetniemi, S.T.: Roman Domination in Graphs. Discrete Mathematics 278, 11–22 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cockayne, E.J., Grobler, P.J.P., Gründlingh, W.R., Munganga, J., van Vuuren, J.H.: Protection of a Graph. Utilitas Mathematica 67, 19–32 (2005)

    MATH  MathSciNet  Google Scholar 

  9. Dehne, F., Fellows, M., Fernau, H., Prieto, E., Rosamond, F.: nonblocker set: Parameterized Algorithmics for minimum dominating set. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 237–245. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  11. Dreyer Jr., P.A.: Applications and Variations of Domination in Graphs. PhD thesis, Rutgers University, New Jersey, USA, PhD Thesis (2000)

    Google Scholar 

  12. Fernau, H.: Parameterized Algorithmics: A Graph-Theoretic Approach. Habilitationsschrift, Universität Tübingen, Germany (2005) (submitted)

    Google Scholar 

  13. Fomin, F.V., Thilikos, D.M.: Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-up. In: Proc. 14th SODA, pp. 168–177 (2003)

    Google Scholar 

  14. Goddard, W.D., Hedetniemi, S.M., Hedetniemi, S.T.: Eternal Security in Graphs. J. Combin. Math. Combin. Comput. (to appear)

    Google Scholar 

  15. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker, New York (1998)

    MATH  Google Scholar 

  16. Henning, M.A.: Defending the Roman Empire from Multiple Attacks. Discrete Mathematics 271, 101–115 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Henning, M.A., Hedetniemi, S.T.: Defending the Roman Empire: a New Strategy. Discrete Mathematics 266, 239–251 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kloks, T. (ed.): Treewidth. LNCS, vol. 842. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  19. Liedloff, M., Kloks, T., Liu, J., Peng, S.-L.: Roman Domination over Some Graphs Classes. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 103–114. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Pagourtzis, A., Penna, P., Schlude, K., Steinhöfel, K., Taylor, D.S., Widmayer, P.: Server Placements, Roman Domination and Other Dominating Set Variants. In: 2nd IFIP International Conference on Theoretical Computer Science IFIP TCS, pp. 280–291. Kluwer, Dordrecht (2002)

    Google Scholar 

  21. Stewart, I.: Defend the Roman Empire! Scientific American, 136–139 (December 1999)

    Google Scholar 

  22. Telle, J.A., Proskurowski, A.: Practical Algorithms on Partial k-Trees with an Application to Domination-Like Problems. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1993. LNCS, vol. 709, pp. 610–621. Springer, Heidelberg (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Hertfordshire, Hatfield, UK

    Henning Fernau

  2. The University of Newcastle, Australia

    Henning Fernau

  3. WSI für Informatik, Universität Tübingen, Germany

    Henning Fernau

Authors
  1. Henning Fernau
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann  & Július Štuller  & 

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

    Gerard Tel

  3. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  4. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fernau, H. (2006). Roman Domination: A Parameterized Perspective. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_24

Download citation

  • DOI: https://doi.org/10.1007/11611257_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31198-0

  • Online ISBN: 978-3-540-32217-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation