In microblog retrieval, query expansion can be essential to obtain good search results due to the short size of queries and posts. Since information in microblogs is highly dynamic, an up-to-date index coupled with pseudo-relevance feedback (PRF) with an external corpus has a higher chance of retrieving more relevant documents and improving ranking. In this paper, we focus on the research question:how can we reduce the query expansion computational cost while maintaining the same retrieval precision as standard PRF? Therefore, we propose to accelerate the query expansion step of pseudo-relevance feedback. The hypothesis is that using an expansion corpus organized into verticals for expanding the query, will lead to a more efficient query expansion process and improved retrieval effectiveness. Thus, the proposed query expansion method uses a distributed search architecture and resource selection algorithms to provide an efficient query expansion process. Experiments on the TREC Microblog datasets show that the proposed approach can match or outperform standard PRF in MAP and NDCG@30, with a computational cost that is three orders of magnitude lower.