Weighted α-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum α and α-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted αrate domination set problem which is, best to our knowledge, the first such algorithm. A theoretical approximation bound based on simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that measures in vertices could be interpreted as the cost of getting those individuals on the board for a campaign or a behaviour change intervention. The minimum weighted α-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least α∗100% of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.