Approximate nearest neighbor search (ANNS) in high-dimensional spaces is a pivotal challenge in the field of machine learning. In recent years, graph-based methods have emerged as the superior approach to ANNS, establishing a new state of the art. Although various optimizations for graph-based ANNS have been introduced, they predominantly rely on heuristic methods that lack formal theoretical backing. This paper aims to enhance routing within graph-based ANNS by introducing a method that offers a probabilistic guarantee when exploring a node's neighbors in the graph. We formulate the problem as probabilistic routing and develop two baseline strategies by incorporating locality-sensitive techniques. Subsequently, we introduce PEOs, a novel approach that efficiently identifies which neighbors in the graph should be considered for exact distance calculation, thus significantly improving efficiency in practice. Our experiments demonstrate that equipping PEOs can increase throughput on commonly utilized graph indexes (HNSW and NSSG) by a factor of 1.6 to 2.5, and its efficiency consistently outperforms the leading-edge routing technique by 1.1 to 1.4 times.
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