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Online Dominating Set

Authors Joan Boyar, Stephan J. Eidenbenz, Lene M. Favrholdt, Michal Kotrbcik, Kim S. Larsen

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Joan Boyar
Stephan J. Eidenbenz
Lene M. Favrholdt
Michal Kotrbcik
Kim S. Larsen

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Joan Boyar, Stephan J. Eidenbenz, Lene M. Favrholdt, Michal Kotrbcik, and Kim S. Larsen. Online Dominating Set. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SWAT.2016.21

Abstract

This paper is devoted to the online dominating set problem and its variants on trees, bipartite, bounded-degree, planar, and general graphs, distinguishing between connected and not necessarily connected graphs. We believe this 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. In most cases, we obtain tight bounds on the competitive ratios. Our results show that requiring the graphs to be presented in a connected fashion allows the online algorithms to obtain provably better solutions. Furthermore, 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.
Keywords
  • online algorithms
  • dominating set
  • competitive analysis
  • graph classes
  • connected graphs

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