Set similarity join, which finds all the similar set pairs from two collections of sets, is a fundamental problem with a wide range of applications. Existing works study both exact set similarity join and approximate similarity join problems. In this paper, we focus on the exact set similarity join problem. The existing solutions for exact set similarity join follow a filtering-verification framework, which generates a list of candidate pairs through scanning indexes in the filtering phase and reports those similar pairs in the verification phase. Though much research has been conducted on this problem, set relations have not been well studied on improving the algorithm efficiency through computational cost sharing. Therefore, in this paper, we explore the set relations in different levels to reduce the overall computational cost. First, it has been shown that most of the computational time is spent on the filtering phase, which can be quadratic to the number of sets in the worst case for the existing solutions. Thus, we explore index-level set relations to reduce the filtering cost while keeping the same filtering power. We achieve this by grouping related sets into blocks in the index and skipping useless index probes in joins. Second, we explore answer-level set relations to further improve the algorithm based on the intuition that if two sets are similar, their answers may have a large overlap. We derive an algorithm which incrementally generates the answer of one set from an already computed answer of another similar set rather than compute the answer from scratch to reduce the computational cost. In addition, considering that in real applications, the data are usually updated dynamically, we extend our techniques and design efficient algorithms to incrementally update the join result when any element in the sets is updated. Finally, we conduct extensive performance studies using 21 real datasets with various data properties from a wide range of domains. The experimental results demonstrate that our algorithm outperforms all the existing algorithms across all datasets.
