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Paper: https://arxiv.org/abs/1603.09320 The provided text details the development of Hierarchical Navigable Small World (HNSW), a graph-based data structure designed for efficient approximate K-nearest neighbour searches. By organizing data into a multi-layered hierarchy, the algorithm allows for a logarithmic complexity scaling, which significantly improves upon the performance of traditional proximity graphs. The system utilizes a stochastic level generation method similar to skip lists, ensuring that search queries can quickly traverse broad scales before refining results in denser layers. To maintain high accuracy in clustered or high-dimensional data, the authors introduce a specialised heuristic for selecting graph connections that preserves global connectivity. Extensive evaluations demonstrate that HNSW outperforms existing state-of-the-art methods across various metrics, including search speed and index construction time. Ultimately, this approach offers a robust and scalable solution for similarity searches in both vector and general metric spaces.