Decomposition plays a significant role in cooperative co-evolution which shows great potential in large scale black-box optimization. However, current popular decomposition algorithms generally require to sample and evaluate a large number of solutions for interdependency detection, which is very time-consuming. To address this issue, this study proposes a new decomposition algorithm named fast differential grouping (FDG). FDG first identifies the type of an instance by detecting the interdependencies of a few pairs of variable subsets selected according to certain rules, and thus can rapidly complete the decomposition of a fully separable or nonseparable instance. For an identified partially separable instance, FDG converts the key decomposition process into a search process in a binary tree by taking corresponding variable subsets as tree nodes. This enables it to directly deduce the interdependency related to a child node by reutilizing the solutions sampled for corresponding parent and brother nodes. To support the above operations, this study designs a normalized variable-subset-oriented interdependency indicator, which can adaptively generate decomposition thresholds according to its distribution and thus enhances decomposition accuracy. Computational complexity analysis and experimental results verify that FDG outperforms popular decomposition algorithms. Further tests indicate that FDG embedded in a cooperative co-evolution framework can achieve highly competitive optimization results as compared with some state-of-the-art algorithms for large scale black-box optimization.