Online Dominating Set.
Joan Boyar, Stephan J. Eidenbenz, Lene M. Favrholdt, Michal Kotrbčík, and Kim S. Larsen.
In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), volume 53 of LIPIcs, pages 21:1-21:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, 2016.
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.

Link to the publication at the publisher's site - subscription may be required.
Text required by the publisher (if any): none.

open access (505 KB)
The same as the publisher's version, when the publisher permits. Otherwise, the author's last version before the publisher's copyright; this is often exactly the same, but sometimes fonts, page numbers, figure numbers, etc. are different. It may also be a full version. However, it is safe to read this version, and at the same time cite the official version, as long as references to concrete locations, numbered theorems, etc. inside the article are avoided.

other publications
Other publications by the author.