Skip to main content
SpringerLink
Log in

Experiments on data reduction for optimal domination in networks

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We present empirical results on computing optimal dominating sets in networks by means of data reduction through efficient preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered data reduction techniques for practically solving one of the most important network problems in combinatorial optimization.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alber, J. (2003). Exact Algorithms for NP-hard Problems on Networks: Design, Analysis, and Implementation. PhD thesis, WSI für Informatik, Universität Tübingen, Germany.

  • Alber, J., H.L. Bodlaender, H. Fernau, T. Kloks, and R. Niedermeier. (2002).“Fixed Parameter Algorithms for Dominating Set and Related Problems on Planar Graphs.” Algorithmica, 33(4), 461–493.

    Article  Google Scholar 

  • Alber, J., H. Fan, M.R. Fellows, H. Fernau, R. Niedermeier, F. Rosamond, and U. Stege. (2005).“ A Refined Search Tree Technique for Dominating Set on Planar Graphs. ” Journal of Computer and System Sciences 71(4), 385–405.

    Google Scholar 

  • Alber, J., M.R. Fellows, and R. Niedermeier. (2004).“Polynomial Time Data Reduction for Dominating Set.” Journal of the ACM, 51(3), 363–384.

    Article  Google Scholar 

  • Bader, G.D., I. Donaldson, C. Wolting, B.F.F. Quellette, T. Pawson, and C.W.V. Hogue. (2001).“BIND—The Biomolecular Interaction Network Database.” Nucleic Acids Research, 29(1), 242–245.

    Article  Google Scholar 

  • Chen, J., H. Fernau, I.A. Kanj, and G. Xia. (2005). “Parametric Duality and Kernelization: Lower Bounds and upper Bounds on Kernel Size.” In Proc. 22d STACS, vol. 3404 of LNCS, Springer, pp. 269–280.

  • Chen, Q., H. Chang, R. Govindan, S. Jamin, S. Shenker, and W. Willinger. (2002).“The Origin of Power-Laws in Internet Topologies Revisited.” In Proc. of INFOCOM.

  • Demaine, E.D. and M. Hajiaghayi. (2005).“Bidimensionality: New Connections Between FPT Algorithms and PTASs.” In Proc. 16th SODA, ACM/SIAM, pp. 590–601.

  • Feige, U. (1998).“A Threshold of ln n for Approximating Set Cover.” Journal of the ACM, 45(4):634–652.

    Article  Google Scholar 

  • Fomin, F.V. and D.M Thilikos. (2003).“Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up.” In Proc. 14th SODA, ACM/SIAM, pp. 168–177.

  • Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman.

  • Guo, J., R. Niedermeier, and D. Raible. (2005).“Improved Algorithms and Complexity Results for Power Domination in Graphs.” In Proc. 15th FCT, volume 3623 of LNCS. Springer pp. 172–184.

  • Haynes, T.W., S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning. (2002).“Domination in Graphs Applied to Electric Power Networks.” SIAM Journal on Discrete Mathematics, 15(4), 519–529.

    Article  Google Scholar 

  • Haynes, T.W., S.T. Hedetniemi, and P.J. Slater. (1998a). Domination in Graphs: Advanced Topics, vol. 209 of Pure and Applied Mathematics. Marcel Dekker.

  • Haynes, T.W., S.T. Hedetniemi, and P.J. Slater. (1998b). Fundamentals of Domination in Graphs, vol. 208 of Pure and Applied Mathematics. Marcel Dekker.

  • Jin, C., Q. Chen, and S. Jamin. (2001).“Inet: Internet Topology Generator.” Technical Report CSE-TR443-00, Department of EECS, University of Michigan.

  • Kratsch, D. (1998).“Algorithms.” In T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, (eds.), Domination in Graphs: Advanced Topics. Marcel Dekker.

  • Medina, A., A. Lakhina, I. Matta, and J.W. Byers. (2001).“Brite: An Approach to Universal Topology Generation.” In Proc. MASCOTS.

  • Mehlhorn, K. and S. Näher. (1999). LEDA: A Platform of Combinatorial and Geometric Computing. Cambridge University Press.

  • Roberts, F.S. (1979). Graph Theory and Its Applications to Problems of Society. SIAM Press, Odyssey Press.

  • Sanchis, L.A. (2002).“Experimental Analysis of Heuristic Algorithms for the Dominating Set problem.” Algorithmica, 33(1), 3–18.

    Article  Google Scholar 

  • Valente, T.W., B.R. Hoffman, A. Ritt-Olson, K. Lichtman, and C.A. Johnson. (2003).“Strategies on Peer-Led Tobacco Prevention Programs in Schools.” American Journal of Public Health, 93(11), 1837–1843.

    Article  Google Scholar 

  • Wan, P.-J., K.M. Alzoubi, and O. Frieder. (2003).“A Simple Heuristic for Minimum Connected Dominating Set in Graphs.” International Journal of Foundations of Computer Science, 14(2), 323–333.

    Article  Google Scholar 

  • Weihe, K. (1998).“Covering Trains by Stations or the Power of Data Reduction.” In Proc. 1st ALEX'98, pp. 1–8.

Download references

Author information

Authors and Affiliations

  1. Power System Applications   Consulting, DIgSILENT GmbH, Heinrich-Hertz-Str.9, D-72810, Gomaringen, Germany

    Jochen Alber

  2. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Nadja Betzler

  3. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Rolf Niedermeier

Authors
  1. Jochen Alber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nadja Betzler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rolf Niedermeier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rolf Niedermeier.

Additional information

Supported by the Deutsche Forschungsgemeinschaft (DFG), project PEAL (parameterized complexity and exact algorithms), NI 369/1 and junior research group PIAF (fixed-parameter algorithms), NI 369/4. Main work done while all authors were with Universität Tübingen. An extended abstract of this paper appeared in the Proceedings of the International Network Optimization Conference (INOC 2003), pages 1–6, held in Evry/Paris, France, October 27–29, 2003.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alber, J., Betzler, N. & Niedermeier, R. Experiments on data reduction for optimal domination in networks. Ann Oper Res 146, 105–117 (2006). https://doi.org/10.1007/s10479-006-0045-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-006-0045-4

Keywords

Search

Navigation