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 whose initial activation would trigger a cascade activating the entire graph. Goldberg and Liu presented an algorithm for this problem that returns a seed set of size O(rl log(n)) times that of an optimum seed set, where r is the diameter of the given graph, and l is the number of distinct thresholds used in the instance. We improve upon this result by presenting an O( min {r,l} log(n))-approximation algorithm. Our algorithm is simple and combinatorial, in contrast with the previous approach that is based on randomized rounding applied to the solution of a linear program.