Social networks are increasingly becoming an outlet that is more and more powerful in spreading news and influence individuals. Compared with other traditional media outlets such as newspaper, radio, and television, social networks empower users to spread their ideological message and/or to deliver target advertising very efficiently in terms of both cost and time. In this article, the authors focus on efficiently finding dominating sets in social networks for the classical dominating set problem as well as for two related problems: partial dominating sets and d-hop dominating sets. They will present algorithms for determining efficiently a good approximation for the social network minimum dominating sets for each of the three variants. The authors ran an extensive suite of experiments to test the presented algorithms on several datasets that include real networks made available by the Stanford Network Analysis Project and synthetic networks that follow the power-law and random models that they generated for this work. The performed experiments show that the selection of the algorithm that performs best to determine efficiently the dominating set is dependent of network characteristics and the order of importance between the size of the dominating set and the time required to determine such a set.
Efficient approximation algorithms for bandwidth consecutive multicolorings of graphs
