Think globally, act locally: On the optimal seeding for nonsubmodular influence maximization

We study the $r$-complex contagion influence maximization problem. In problem, one chooses a fixed number of initial seeds in social network to maximize spread their influence. model, each uninfected vertex becomes infected if it has at least $r$ neighbors. this paper, we focus on random graph model named stochastic hierarchical blockmodel, which is special case well-studied blockmodel. When not exceptionally sparse, particular, when edge appears with probability $\omega(n^{-(1+1/r)})$, under certain mild assumptions, prove that optimal seeding strategy put all single community. This matches intuition nonsubmodular cascade placing near other creates synergy. However, sharply contrasts for submodular models (e.g., independent and linear threshold model) nearby tend erode others' effects. Our key technique novel time-asynchronized coupling four processes. Finally, show observation yields polynomial time dynamic programming algorithm outputs either $\omega(n^{-(1+1/r)})$ or $o(n^{-2})$.