1 research outputs found
Efficient Spatial Nearest Neighbor Queries Based on Multi-layer Voronoi Diagrams
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