Better Approximation Algorithms for Technology Diffusion

Motivated by cascade effects arising in network technology upgrade processes in the Internet, Goldberg and Liu [SODA, 2013] recently introduced the following natural technology diffusion problem. Given a graph G = (V,E), and thresholds θ(v), for all v ∈ V. A vertex u activates if it is adjacent to a connected component of active nodes of size at least θ(v). The goal is to find a seed set \(\mathcal{A}\) whose initial activation would trigger a cascade activating the entire graph.