Inverse Queries For Multidimensional Spaces

TL;DR

This paper introduces inverse spatial queries, which find objects that would include a given set of objects in their results, and presents a framework to efficiently answer these queries across various predicates.

Contribution

The paper defines inverse spatial queries and develops a filter-and-refinement framework to improve their efficiency across multiple query types.

Findings

The framework significantly outperforms naive approaches.

Efficient solutions are provided for inverse epsilon range, k-NN, and skyline queries.

Experimental results demonstrate substantial efficiency gains.

Abstract

Traditional spatial queries return, for a given query object $q$, all database objects that satisfy a given predicate, such as epsilon range and $k$-nearest neighbors. This paper defines and studies {\em inverse} spatial queries, which, given a subset of database objects $Q$ and a query predicate, return all objects which, if used as query objects with the predicate, contain $Q$ in their result. We first show a straightforward solution for answering inverse spatial queries for any query predicate. Then, we propose a filter-and-refinement framework that can be used to improve efficiency. We show how to apply this framework on a variety of inverse queries, using appropriate space pruning strategies. In particular, we propose solutions for inverse epsilon range queries, inverse $k$-nearest neighbor queries, and inverse skyline queries. Our experiments show that our framework is significantly more efficient than naive approaches.