TipTop: Exact Solutions for Influence Maximization in Billion-scale Networks

In this paper, we study the Cost-aware Target Viral Marketing (CTVM) problem, a generalization of Influence Maximization (IM), a well-known problem in viral marketing. CTVM asks for the most cost-effective users to influence the most relevant users. Instead of approximating the problem as done in the literature, we attempt to offer exact solutions. As the problem is in NP-hard, clearly the exact solution is not in polynomial time, thus the most challenge is to design the scalable exact solution, which can be run on large-scale networks. We first highlight that using a traditional two stage stochastic programming to exactly solve CTVM is not possible because of scalability. We then propose our solution TIPTOP, which has an approximation ratio of (1− ). This result significantly improves the current best solutions to both IM and CTVM. At the heart of TIPTOP lies an innovative technique that reduces the number of samples as much as possible. This allows us to exactly solve CTVM on a much smaller space of generated samples using Integer Programming. While obtaining an almost exact solution, TIPTOP is very scalable, running on billion-scale networks such as Twitter. Furthermore, TIPTOP lends a tool for researchers to benchmark their solutions against the optimal one in large-scale networks, which is currently not available. Keywords—Viral Marketing; Influence Maximization; Algorithms; Online Social Networks; Optimization