Solving Influence Maximization Problem under Deterministic Linear Threshold Model Using Metaheuristic Optimization

In the paper we consider the discrete variant of the well-known Influence Maximization Problem (IMP). Given some influence model, it consists in finding a so-called seed set of influential users of fixed size, that maximizes the total spread of influence over the network. We limit our study to the influence model called Deterministic Linear Threshold Model (DLTM). It is well known that IMP under DLTM is computationally hard and there are no approximate algorithms for its solving with a constant approximation ratio if $P\neq NP$. Therefore, it makes sense to apply metaheuristic algorithms to this problem. In the present research we propose new algorithms for solving IMP under DLTM, which are based on a technique that combines evolutionary and genetic strategies for pseudo-Boolean optimization with a greedy algorithm which is used to find some initial approximation. We use the proposed strategy to solve another well-known combinatorial problem for networks called Target Set Selection (TSS). We propose to solve TSS as a sequence of IMPs with gradually decreasing of target set size. In the experimental part of the paper we demonstrate that our new strategy outperforms the previous ways to solve TSS, yielding smaller target sets of good quality.