, Volume 81, Issue 5, pp 1938–1964 | Cite as

Online Dominating Set

  • Joan Boyar
  • Stephan J. Eidenbenz
  • Lene M. Favrholdt
  • Michal Kotrbčík
  • Kim S. LarsenEmail author


This paper is devoted to the online dominating set problem and its variants. We believe the paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing the future, and being incremental, i.e., having to maintain solutions to all prefixes of the input. This is quantified through competitive analyses of online algorithms against two optimal algorithms, both knowing the entire input, but only one having to be incremental. We also consider the competitive ratio of the weaker of the two optimal algorithms against the other. We consider important graph classes, distinguishing between connected and not necessarily connected graphs. For the classic graph classes of trees, bipartite, planar, and general graphs, we obtain tight results in almost all cases. We also derive upper and lower bounds for the class of bounded-degree graphs. From these analyses, we get detailed information regarding the significance of the necessary requirement that online algorithms be incremental. In some cases, having to be incremental fully accounts for the online algorithm’s disadvantage.


Online algorithms Dominating set Competitive analysis Irrevocability 



The authors would like to thank an anonymous referee for constructive suggestions.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Joan Boyar
    • 1
  • Stephan J. Eidenbenz
    • 2
  • Lene M. Favrholdt
    • 1
  • Michal Kotrbčík
    • 3
  • Kim S. Larsen
    • 1
    Email author
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  2. 2.Los Alamos National LaboratoryLos AlamosUSA
  3. 3.School of Mathematics and PhysicsUniversity of QueenslandBrisbaneAustralia

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