The Unified Segment Tree and its Application to the Rectangle Intersection Problem

TL;DR

This paper introduces a unified multidimensional segment tree that simplifies solving the rectangle intersection problem by unifying different dimensional interpretations, enabling new applications and more straightforward solutions.

Contribution

The paper presents a novel variation of the multidimensional segment tree with new definitions and properties that facilitate solving the rectangle intersection problem more naturally.

Findings

Unified segment tree concept introduced

Properties enable new application scenarios

Simpler solution for rectangle intersection problem

Abstract

In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that arise naturally in this variation, and we show some properties concerning the relationships between the nodes, and the regions those nodes represent. We think these properties will enable the data to be utilized in new situations, beyond those previously studied. As an example, we show that the data structure can be used to solve the Rectangle Intersection Problem in a more straightforward and natural way than had be done in the past.