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.