- 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.
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