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 all arbitrary social network of size a using O(n(2)) queries, matching the information theoretic lower bound 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 Theta(n log(n)) queries. We also give all approximation algorithm for finding ail influential set of nodes in the network; without resorting to learning its structure. Finally, we discuss some limitation of our approach and limitations of path-based methods, when non-exact value injection queries are used.