Hierarchical navigable small world (HNSW) algorithms enhance search efficiency in high-dimensional data by organizing data points into layered graphs, which significantly reduces search complexity while maintaining high recall. Unlike other approximate nearest neighbor (ANN) methods, HNSW offers a practical solution without requiring a training phase, making it ideal for applications like image recognition, natural language processing, and recommendation systems. However, it does come with challenges such as high memory consumption and computational overhead during index construction.

A search engine performs two main tasks: retrieval, which involves finding documents that satisfy a query, and ranking, which determines the best matches. This article focuses on retrieval, explaining the use of forward and inverted indexes for efficient document searching and the concept of set intersection as a fundamental operation in retrieval processes.