Advertisement

Solving Capacitated Dominating Set by Using Covering by Subsets and Maximum Matching

  • Mathieu Liedloff
  • Ioan Todinca
  • Yngve Villanger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

The Capacitated Dominating Set problem is the problem of finding a dominating set of minimum cardinality where each vertex has been assigned a bound on the number of vertices it has capacity to dominate. Cygan et al. showed in 2009 that this problem can be solved in \(O(n^3 m {{n} \choose {n/3}})\) or in O *(1.89 n ) time using maximum matching algorithm. An alternative way to solve this problem is to use dynamic programming over subsets. By exploiting structural properties of instances that can not be solved fast by the maximum matching approach, and “hiding” additional cost related to considering subsets of large cardinality in the dynamic programming, an improved algorithm is obtained. We show that the Capacitated Dominating Set problem can be solved in O *(1.8463 n ) time.

Keywords

Dynamic Programming Maximum Match Polynomial Term Capacity Function Polynomial Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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(4), 461–493 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bodlaender, H.L., Lokshtanov, D., Penninkx, E.: Planar capacitated dominating set is W[1]-Hard. In: Chen and Fomin [3], pp. 50–60Google Scholar
  3. 3.
    Chen, J., Fomin, F.V. (eds.): 4th International Workshop on Parameterized and Exact Computation, IWPEC 2009, Copenhagen, Denmark, Revised Selected Papers, September 10-11. LNCS, vol. 5917. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  4. 4.
    Cygan, M., Pilipczuk, M., Wojtaszczyk, J.O.: Capacitated domination faster than O(2n). In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 74–80. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Fomin, F.V., Grandoni, F., Kratsch, D.: Solving connected dominating set faster than 2n. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 152–163. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Fomin, F.V., Iwama, K., Kratsch, D., Kaski, P., Koivisto, M., Kowalik, L., Okamoto, Y., van Rooij, J., Williams, R.: 08431 open problems moderately exponential time algorithms. In: Fomin, F.V., Iwama, K., Kratsch, D. (eds.) Moderately Exponential Time Algorithms. No. 08431 in Dagstuhl Seminar Proceedings, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, Dagstuhl, Germany (2008), http://drops.dagstuhl.de/opus/volltexte/2008/1798
  8. 8.
    Fomin, F.V., Kratsch, D., Woeginger, G.J.: Exact (exponential) algorithms for the dominating set problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 245–256. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Koivisto, M.: Partitioning into sets of bounded cardinality. In: Chen and Fomin [3], pp. 258–263Google Scholar
  10. 10.
    van Rooij, J.M.M., Nederlof, J., van Dijk, T.C.: Inclusion/exclusion meets measure and conquer. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 554–565. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mathieu Liedloff
    • 1
  • Ioan Todinca
    • 1
  • Yngve Villanger
    • 2
  1. 1.LIFOUniversité d’OrléansOrléans Cedex 2France
  2. 2.Department of InformaticsUniversity of BergenBergenNorway

Personalised recommendations