Periortree: An Extention of R-Tree for Periodic Boundary Conditions

TL;DR

This paper introduces a novel extension of the R-Tree data structure tailored for efficient spatial searches under periodic boundary conditions, eliminating the need for extra objects or queries and improving bounding box volume reduction.

Contribution

The proposed method extends R-Tree to handle periodic boundaries without additional objects, enhancing efficiency and applicability to other bounding box-based structures.

Findings

Reduces bounding box volume under periodic conditions

No extra objects or queries needed

Applicable to other spatial data structures

Abstract

Searching spatial data is an important operation for scientific simulations which are performed mostly with periodic boundary conditions. An R-Tree is a well known tree data structure used to contain spatial objects and it is capable of answering to spatial searching queries in an efficient way. In this paper, a novel method to construct an R-Tree considering periodic boundary conditions is presented. Unlike existing methods, the proposed method works without any kind of extra objects or queries. Moreover, because this method reduces the volume of bounding box for each node under the periodic boundary conditions, it is expected to increase the overall efficiency. While the extension of an R-Tree is presented in this work, this method is not only applicable to an R-Tree but also to other data structures that use axis-aligned bounding boxes with periodic boundary conditions. The implementation is available on GitHub.