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Multi-set membership query is a fundamental issue for network functions such as packet processing and state machines monitoring. Given the rigid query speed and memory requirements, it would be promising if a multi-set query algorithm can be designed based on Bloom filter (BF), a space-efficient probabilistic data structure. However, existing efforts on multi-set query based on BF suffer from at least one of the following drawbacks: low query speed, low query accuracy, limitation in only supporting insertion and query operations, or limitation in the set size. To address the issues, we design a novel B h sequence-based Bloom filter (B h BF) for multi-set query, which supports four operations: insertion, query, deletion, and update. In B h BF, the set ID is encoded as a code in a B h sequence. Exploiting good properties of B h sequences, we can correctly decode the BF cells to obtain the set IDs even when the number of hash collisions is high, which brings high query accuracy. In B h BF, we propose two strategies to further speed up the query speed and increase the query accuracy. On the theoretical side, we analyze the false positive and classification failure rate of our B h BF. Our results from extensive experiments over two real datasets demonstrate that B h BF significantly advances state-of-the-art multi-set query algorithms.

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