In this paper, we study the problem of approximate containment similarity search. Given two records Q and X, the containment similarity between Q and X with respect to Q is |Q intersect X|/ |Q|. Given a query record Q and a set of records S, the containment similarity search finds a set of records from S whose containment similarity regarding Q are not less than the given threshold. This problem has many important applications in commercial and scientific fields such as record matching and domain search. Existing solution relies on the asymmetric LSH method by transforming the containment similarity to well-studied Jaccard similarity. In this paper, we use a different framework by transforming the containment similarity to set intersection. We propose a novel augmented KMV sketch technique, namely GB-KMV, which is data-dependent and can achieve a good trade-off between the sketch size and the accuracy. We provide a set of theoretical analysis to underpin the proposed augmented KMV sketch technique, and show that it outperforms the state-of-the-art technique LSH-E in terms of estimation accuracy under practical assumption. Our comprehensive experiments on real-life datasets verify that GB-KMV is superior to LSH-E in terms of the space-accuracy trade-off, time-accuracy trade-off, and the sketch construction time. For instance, with similar estimation accuracy (F-1 score), GB-KMV is over 100 times faster than LSH-E on some real-life dataset.

Abstract In this paper, we study the problem of selectivity estimation on set containment search. Given a query record Q and a record dataset $${\mathcal {S}}$$ S , we aim to accurately and efficiently estimate the selectivity of set containment search of query Q over $${\mathcal {S}}$$ S . We first extend existing distinct value estimating techniques to solve this problem and develop an inverted list and G-KMV sketch-based approach IL-GKMV. We analyze that the performance of IL-GKMV degrades with the increase in vocabulary size. Motivated by limitations of existing techniques and the inherent challenges of the problem, we resort to developing effective and efficient sampling approaches and propose an ordered trie structure-based sampling approach named OT-Sampling. OT-Sampling partitions records based on element frequency and occurrence patterns and is significantly more accurate compared with simple random sampling method and IL-GKMV. To further enhance the performance, a divide-and-conquer-based sampling approach, DC-Sampling, is presented with an inclusion/exclusion prefix to explore the pruning opportunities. Meanwhile, we consider weighted set containment selectivity estimation and devise stratified random sampling approach named StrRS. We theoretically analyze the proposed techniques regarding various accuracy estimators. Our comprehensive experiments on nine real datasets verify the effectiveness and efficiency of our proposed techniques.