Online Dominating Set

Joan Boyar, Stephen J. Eidenbenz, Lene Monrad Favrholdt, Michal Kotrbcik, Kim Skak Larsen

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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.
Original languageEnglish
Title of host publication15th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2016
EditorsRasmus Pagh
PublisherSchloss Dagstuhl-Leibniz-Zentrum fuer Informatik
Publication date2016
Pages1-15
Article number21
ISBN (Electronic)978-3-95977-011-8
DOIs
Publication statusPublished - 2016
Event15th Scandinavian Symposium and Workshops on Algorithm Theory - Reykjavik, Iceland
Duration: 22. Jun 201624. Jun 2016

Conference

Conference15th Scandinavian Symposium and Workshops on Algorithm Theory
Country/TerritoryIceland
CityReykjavik
Period22/06/201624/06/2016
SeriesLeibniz International Proceedings in Informatics
Volume53
ISSN1868-8969

Keywords

  • Competitive analysis
  • Connected graphs
  • Dominating set
  • Graph classes
  • Online algorithms

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