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Influence maximization is a problem of finding a small set of highlyinfluential users, also known as seeds, in a social network such that thespread of influence under certain propagation models is maximized. In thispaper, we consider time-critical influence maximization, in which one wants tomaximize influence spread within a given deadline. Since timing is consideredin the optimization, we also extend the Independent Cascade (IC) model and theLinear Threshold (LT) model to incorporate the time delay aspect of influencediffusion among individuals in social networks. We show that time-criticalinfluence maximization under the time-delayed IC and LT models maintainsdesired properties such as submodularity, which allows a greedy approximationalgorithm to achieve an approximation ratio of $1-1/e$. To overcome theinefficiency of the greedy algorithm, we design two heuristic algorithms: thefirst one is based on a dynamic programming procedure that computes exactinfluence in tree structures and directed acyclic subgraphs, while the secondone converts the problem to one in the original models and then appliesexisting fast heuristic algorithms to it. Our simulation results demonstratethat our algorithms achieve the same level of influence spread as the greedyalgorithm while running a few orders of magnitude faster, and they alsooutperform existing fast heuristics that disregard the deadline constraint anddelays in diffusion.

Time-Critical Influence Maximization in Social Networks with Time-Delayed Diffusion Process