STEM ² : A Fast and Space-efficient Data Structure for Exact Multi-Set Membership Queries

Multi-set membership queries are ubiquitous in networking and database systems. Current solutions force a difficult compromise: hash tables guarantee correctness but suffer from high memory footprints, while filter-based approaches optimize space at the cost of probabilistic errors. In this paper, we propose STEM ² , a fast and space-efficient data structure that achieves 100% query accuracy and can support dynamic key updates for multi-set membership queries. STEM ² utilizes a balanced binary tree architecture where each non-leaf node incorporates a novel Exact Binary Set Separator (XBSS) to partition keys into two disjoint groups. A key innovation of our design is a minimized hashing scheme that requires only two hash computations per key lookup, significantly reducing computational overhead. Additionally, STEM ² separates the control plane and the data plane: the control plane handles construction and dynamic updates, while the data plane is dedicated to serving efficient membership queries. Extensive experiments show that STEM ² achieves over 120 million operations per second (Mops) in lookup throughput, outperforming the state-of-the-art Coloring Embedder by 20% and the Ludo hashing by up to 21.6×, while maintaining compact memory cost and exact correctness.