HNSW

HNSW (Hierarchical Navigable Small World) is a state-of-the-art graph-based algorithm: it executes Approximate Nearest Neighbor (ANN) search on high-dimensional vectors with logarithmic complexity (O(log n)), ensuring lightning-fast similarity retrieval.

Hierarchical Navigable Small World (HNSW) is the dominant Approximate Nearest Neighbor (ANN) search algorithm, delivering superior speed and recall for vector databases. It constructs a multi-layer proximity graph: higher layers contain long-range connections for rapid traversal, while lower layers provide fine-grained accuracy for finding the true nearest neighbors. This hierarchical structure, detailed in the 2016 paper by Malkov and Yashunin, achieves logarithmic complexity scaling, making it highly efficient. Use it to power critical applications like large-scale image retrieval, real-time product recommendation engines, and modern Retrieval-Augmented Generation (RAG) systems.

https://arxiv.org/abs/1603.09320