Online Dominating Set
- 26 Downloads
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.
KeywordsOnline algorithms Dominating set Competitive analysis Irrevocability
The authors would like to thank an anonymous referee for constructive suggestions.
- 4.Böhm, M., Sgall, J., Veselý, P.: Online colored bin packing. In: Bampis, E., Svensson, O. (eds.) 12th International Workshop on Approximation and Online Algorithms (WAOA), Lecture Notes in Computer Science, vol. 8952, pp. 35–46. Springer, Berlin (2015)Google Scholar
- 7.Chrobak, M., Sgall, J., Woeginger, G.J.: Two-bounded-space bin packing revisited. In: Demetrescu, C., Halldórsson, M.M. (eds.) 19th Annual European Symposium on Algorithms (ESA), Lecture Notes in Computer Science, vol. 6942, pp. 263–274. Springer, Berlin (2011)Google Scholar
- 9.Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. IEEE Int. Conf. Commun. 1, 376–380 (1997)Google Scholar
- 20.Ore, O.: Theory of graphs. In: Colloquium Publications, vol. 38, American Mathematical Society, Providence (1962)Google Scholar