Closest Pair Queries with Spatial Constraints

Abstract

Given two datasets $\mathcal{D}_{A}$ and $\mathcal{D}_{B}$ the closest-pair query (CPQ) retrieves the pair (a,b), where $a \epsilon \mathcal{D}_{A}$ and $b \epsilon \mathcal{D}_{B}$, having the smallest distance between all pairs of objects. An extension to this problem is to generate the k closest pairs of objects (k-CPQ). In several cases spatial constraints are applied, and object pairs that are retrieved must also satisfy these constraints. Although the application of spatial constraints seems natural towards a more focused search, only recently they have been studied for the CPQ problem with the restriction that $\mathcal{D}_{A}$ = $\mathcal{D}_{B}$. In this work we focus on constrained closest-pair queries (CCPQ), between two distinct datasets $\mathcal{D}_{A}$ and $\mathcal{D}_{B}$, where objects from $\mathcal{D}_{A}$ must be enclosed by a spatial region R. A new algorithm is proposed, which is compared with a modified closest-pair algorithm. The experimental results demonstrate that the proposed approach is superior with respect to CPU and I/O costs.