Optimally learning social networks with activations and suppressions

In this paper we consider the problem of learning hidden independent cascade social networks using exact value injection queries. These queries involve activating and suppressing agents in the target network. We develop an algorithm that optimally learns an arbitrary social network of size n using O(n2) queries, matching the information theoretic lower bound that we prove for this problem. We also consider the case when the target social network forms a tree and show that the learning problem takes Θ(nlog(n)) queries. We also give an approximation algorithm for finding an influential set of nodes in the network, without resorting to learning its structure. Finally, we discuss some limitations of our approach, and limitations of path-based methods, when non-exact value injection queries are used.