Abstract:
Influence Maximization Problem involves nding a set of individuals in a social network to trigger an in uence/information spread, i.e., a seed set, such that the maximum possible number of individuals are in uenced. In this thesis, two competitive variants of the Influence Maximization Problem where two players make decisions sequentially in the form of a Stackelberg game are introduced. In the Influence Maximization with Deactivation the objectives of the leader and the follower are maximization and minimization of the spread, respectively. While the Misinformation Spread Minimization Problem has a reverse situation, in both problems the leader takes the follower's optimal response into account. Both problems are formulated as mixed-integer bilevel linear programs with a two-stage stochastic program in the lower level, by enumerating the diffusion scenarios due to the well known Linear Threshold model. In the solution phase, firstly several matheuristic methods are proposed where the follower's optimal decisions are approximated via Sample Average Approximation method. For the MSMP, additionally a state-of-the art in uence maximization method is integrated into the developed algorithms. The proposed methods are evaluated on small instances where an optimal solution can be found via complete enumeration as well as larger instances where the algorithms are compared to each other. Then, a branch-and-cut algorithm for mixed-integer bilevel problems is enriched with a variable bound update procedure for the Influence Maximization with Deactivation which is shown to increase the time effciency. An exact algorithm for bilevel interdiction problems is improved substantially, tested on various problem types including the Misinformation Spread Minimization Problem and yields signi cantly better results.
