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Diffusion processes in complex dynamic networks can arise, for instance, on data search, data routing, and information spreading. Therefore, understanding how to speed up the diffusion process is an important topic in the study of complex dynamic networks. In this paper, we shed light on how centrality measures and node dynamics coupled with simple diffusion models can help on accelerating the cover time in dynamic networks. Using data from systems with different characteristics, we show that if dynamics is disregarded, network cover time is highly underestimated. Moreover, using centrality accelerates the diffusion process over a different set of complex dynamic networks when compared with the random walk approach. For the best case, in order to cover 80% of nodes, fast centrality-driven diffusion reaches an improvement of 60%, i.e. when next-hop nodes are selected by using centrality measures. Additionally, we also propose and present the first results on how link prediction can help on speeding up the diffusion process in dynamic networks.