Efficient Spatial Nearest Neighbor Queries Based on Multi-layer Voronoi Diagrams

TL;DR

This paper introduces a multi-layer Voronoi diagram (MVD) based spatial index that efficiently solves nearest neighbor and k-nearest neighbors queries with logarithmic time complexity, outperforming traditional tree-based indices especially in uneven data distributions.

Contribution

The paper proposes a novel non-tree multi-layer Voronoi diagram index that overcomes limitations of tree-like structures for spatial queries, achieving stable, efficient NN and kNN searches.

Findings

MVD index achieves logarithmic query time for NN and kNN searches.

Experimental results show MVD outperforms VoR-tree, R-tree, and kd-tree in efficiency.

MVD handles uneven data distributions more effectively than traditional indices.

Abstract

Nearest neighbor (NN) problem is an important scientific problem. The NN query, to find the closest one to a given query point among a set of points, is widely used in applications such as density estimation, pattern classification, information retrieval and spatial analysis. A direct generalization of the NN query is the k nearest neighbors (kNN) query, where the k closest point are required to be found. Since NN and kNN problems were raised, many algorithms have been proposed to solve them. It has been indicated in literature that the only method to solve these problems exactly with sublinear time complexity, is to filter out the unnecessary spatial computation by using the pre-processing structure, commonly referred to as the spatial index. The recently proposed spatial indices available for NN search, are almost constructed through spatial partition. These indices are tree-like, and the tree-like hierarchical structure can usually significantly improve the efficiency of NN search. However, when the data are distributed extremely unevenly, it is difficult to satisfy both the balance of the tree and the non-overlap of the subspace corresponding to the nodes. Thus the acceleration performance of the tree-like indices is severely jeopardized. In this paper, we propose a non-tree spatial index which consists of multiple layers of Voronoi diagrams (MVD). This index can entirely avoid the dilemma tree-like structures face, and solve the NN problems stably with logarithmic time complexity. Furthermore, it is convenient to achieve kNN search by extending NN search on MVD. In the experiments, we evaluate the efficiency of this indexing for both NN search and kNN search by comparing with VoR-tree, R-tree and kd-tree. The experiments indicate that compared to NN search and kNN search with the other three indices, these two search methods have significantly higher efficiency with MVD.