Set Similarity - Calculate Jaccard index without quadratic complexity
An option would be to use the Signature Scheme of [1], size-based filtering: a scheme which uses size information to reduce the number of set pairs that need to be considered.

They also experiment with a weighted form; where weights are IDF-based.

[1] Arasu, Arvind, Venkatesh Ganti, and Raghav Kaushik. “Efficient Exact Set-similarity Joins.” In Proceedings of the 32nd International Conference on Very Large Data Bases, 918–929. VLDB  ’06. VLDB Endowment, 2006