Set intersection is a fundamental operation in many applications, such as common neighbor computation in graph-based algorithms, set similarity computation, item recommendation, etc. In the literature, many set intersection methods are proposed. We observe that the state-of-the-art algorithm${\sf RCode}$bears several limitations, such as high index time complexity, inefficient for large-sized sets, and not friendly to the generic set intersection. In this paper, we introduce theBucket Signature forSet(${\sf BigSet}$), an efficient generic set intersection algorithm.${\sf BigSet}$consists of two phases, namely the preprocessing phase and the query phase. In the preprocessing phase,${\sf BigSet}$partitions the elements of a record into$O(2^{k})$buckets and uses a bitmap to indicate the status of the buckets where$n$is the record length and$k$is the number of bits in the signature. In the query phase,${\sf BigSet}$calculates the results using a candidate generating-and-verification framework. Specifically, a set of candidate elements is identified as those falling in the same buckets. Then, for each bucket,${\sf BigSet}$collects the common elements using a merge-based method. To improve the performance, we introduce two optimizations, including bucket sharing and size-aware signature construction techniques. We conduct experiments on 10 real graph datasets and 5 real generic set datasets to evaluate the performance of our proposals. The experiment results show that${\sf BigSet}$is 20× faster than the leading generic set intersection algorithms. Besides it outperforms the${\sf RCode}$with 5× speedup, and while uses up to 8× less memory.