Complete and Sufficient Spatial Domination of Multidimensional Rectangles

TL;DR

This paper introduces a complete and efficient criterion for determining spatial domination among multidimensional rectangles, improving decision accuracy in high-dimensional spaces for applications like nearest neighbor search.

Contribution

It presents a necessary and sufficient decision criterion for spatial domination that overcomes limitations of minimum and maximum distance methods, with practical implementation details.

Findings

Provides a new criterion for spatial domination detection

Efficiently applicable in high-dimensional spaces

Includes pseudocode and Python implementation

Abstract

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A may, must, or must not be closer to objects in a second rectangle B, than objects in a third rectangle R. To decide this relation of "Spatial Domination" it can be shown that using minimum and maximum distances it is often impossible to detect spatial domination. This spatial gem provides a necessary and sufficient decision criterion for spatial domination that can be computed efficiently even in higher dimensional space. In addition, this spatial gem provides an example, pseudocode and an implementation in Python.