We propose a generalized framework for influence maximization in large-scale, time evolving networks. Many real-life influence graphs such as social networks, telephone networks, and IP traffic data exhibit dynamic characteristics, e.g., the underlying structure and communication patterns evolve with time. Correspondingly, we develop a dynamic framework for the influence maximization problem, where we perform effective local updates to quickly adjust the top-k influencers, as the structure and communication patterns in the network change. We design a novel N-Family method (N=1, 2, 3, …) based on the maximum influence arborescence (MIA) propagation model with approximation guarantee of (1 − 1/e). We then develop heuristic algorithms by extending the N-Family approach to other information propagation models (e.g., independent cascade) and influence maximization algorithms (e.g., CELF, reverse reachable sketch). Based on a detailed empirical analysis over several real-world, dynamic, and large-scale networks, we find that our proposed solution, N-Family improves the updating time of the top-k influencers by 1 ∼ 2 orders of magnitude, compared to existing algorithms, while ensuring similar memory usage and influence spreads.