A Bloom filter is a compact and randomized data structure popularly used for networking applications. A standard Bloom filter only answers yes/no questions about membership, but recent studies have improved it so that the value of a queried item can be returned, supporting multiple-set membership testing. In this paper, we design a new data structure for multiple-set membership testing, Bloom tree, which not only achieves space compactness, but also operates more efficiently than existing ones. For example, when existing work requires 107 bits per item and 11 memory accesses for a search operation, a Bloom tree requires only 47 bits and 8 memory accesses. The advantages come from a new data structure that consists of multiple Bloom filters in a tree structure. We study a theoretical analysis model to find optimal parameters for Bloom trees, and its effectiveness is verified through experiments.
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