HVS: Hierarchical Graph Structure Based on Voronoi Diagrams for Solving Approximate Nearest Neighbor Search

Approximate nearest neighbor search (ANNS) is a fundamental problem that has a wide range of applications in information retrieval and data mining. Among state-of-the-art in-memory ANNS methods, graph-based methods have attracted particular interest owing to their superior efficiency and query accuracy. Most of these methods focus on the selection of edges to shorten the search path, but do not pay much attention to the computational cost at each hop. To reduce the cost, we propose a novel graph structure called HVS. HVS has a hierarchical structure of multiple layers that corresponds to a series of subspace divisions in a coarse-to-fine manner. In addition, we utilize a virtual Voronoi diagram in each layer to accelerate the search. By traversing Voronoi cells, HVS can reach the nearest neighbors of a given query efficiently, resulting in a reduction in the total search cost. Experiments confirm that HVS is superior to other state-of-the-art graph-based methods.