Proposed Method

 In this paper, we propose a novel method for indexing spatial data by utilizing a class of mapping functions. Let $\vec{X}=(X_0, ..., X_{n-1})$ be a feature vector in n-dimensional space, and $H_i^n(\vec{X}), \hspace{0.4em}i \hspace{0.4em} \epsilon \hspace{0.4em} \mathcal{N}$ be a class of $\mathcal{D}_n \mapsto \mathcal{D}_1$ functions, such that they map an n-dimensional vector, $\vec{X}$ onto linear space.

In our method, we use the above mapping functions to decompose the n-dimensional space and map each block in the decomposed space onto linear space. Data buckets are assigned to each address of the linear space. So that, by computing the mapping function, we can find the corresponding data bucket for any data point. In insertion and searching, we use that method to locate the data bucket for the target data object. The mapping functions, themselves are stored in the structure.