Dual-Branch HNSW Approach with Skip Bridges and LID-Driven Optimization

Abstract: The Hierarchical Navigable Small World (HNSW) algorithm is widely used for approximate nearest neighbor (ANN) search, leveraging the principles of navigable small-world graphs. However, it faces some limitations. The first is the local optima problem, which arises from the algorithm's greedy search strategy, selecting neighbors based solely on proximity at each step. This often leads to cluster disconnections. The second limitation is that HNSW frequently fails to achieve logarithmic complexity, particularly in high-dimensional datasets, due to the exhaustive traversal through each layer. To address these limitations, we propose a novel algorithm that mitigates local optima and cluster disconnections while enhancing the construction speed, maintaining inference speed. The first component is a dual-branch HNSW structure with LID-based insertion mechanisms, enabling traversal from multiple directions. This improves outlier node capture, enhances cluster connectivity, accelerates construction speed and reduces the risk of local minima. The second component incorporates a bridge-building technique that bypasses redundant intermediate layers, maintaining inference and making up the additional computational overhead introduced by the dual-branch structure. Experiments on various benchmarks and datasets showed that our algorithm outperforms the original HNSW in both accuracy and speed. We evaluated six datasets across Computer Vision (CV), and NLP, showing recall improvements of 18\% in NLP, and up to 30\% in CV tasks while reducing the construction time by up to 20\% and maintaining the inference speed. We did not observe any trade-offs in our algorithm. Ablation studies revealed that LID-based insertion had the greatest impact on performance, followed by the dual-branch structure and bridge-building components.