Minimizing the misinformation spread in social networks

Improved x-space Algorithm for Min-Max Bilevel Integer Programming with an Application to Misinformation Spread in Social Networks

“…A recent survey on influence maximization problems can be found in Li et al (2018). Tanınmış et al (2019) address a competitive version of the IMP in the form of a Stackelberg game where the leader of the game protects a subset of nodes and then the follower activates a set of unprotected nodes (seed set) to start a diffusion process. The aim of the follower is to maximize the expected number of influenced nodes, i.e.…”

“…Finally, Constraint (32) and Constraint (38) are binary restrictions on the decision variables. Note that R is defined as the set of all possible scenarios in Tanınmış et al (2019), so that the distribution of the number of influenced nodes is identical to the one in the LT model. Since the size of R is exhaustive for even very small networks, an approximation method is used to solve the follower's problem whereas the leader's problem is attacked with an heuristic.…”

“…Fischetti et al (2019) develop a branch-and-cut algorithm for interdiction problems whose lower level problem satisfies the down-monotonicity assumption which is also necessary for one of the gen-eral MIBLP algorithms proposed in Tang et al (2016). This assumption restricts the applicability of the algorithm since it is violated in some important applications including the misinformation spread minimization (Tanınmış et al, 2019). The x-space algorithm devised in Tang et al (2016), however, which is shown to outperform the other two algorithms in the same paper, does not make this assumption, and becomes the starting point for the research in the present paper.…”

“…The second contribution is the application of the improved x-space algorithm to exactly solve the Misinformation Spread Minimization Problem (MSMP) for which only heuristics are proposed so far Tanınmış et al (2019). In this problem, which is defined in the context of a social network, the leader protects h nodes, and the follower subsequently activates k nodes among unprotected ones to start a diffusion process.…”

“…In fact, it is a stochastic interdiction problem where the leader interdicts (prevents) the activation of a set of nodes by the follower. The bilevel formulation proposed in Tanınmış et al (2019) does not have the required structure for the design of the modified algorithm. Nevertheless, the application becomes possible via reformulation and utilizing some problem specific features.…”