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Related Experiment Video

Updated: Jun 23, 2026

Collecting and Processing Drone-based Remotely Sensed Data for Use in Forest Recovery Monitoring

Collecting and Processing Drone-based Remotely Sensed Data for Use in Forest Recovery Monitoring

Published on: October 24, 2025

A constant-time algorithm for finding neighbors in quadtrees.

Kunio Aizawa¹, Shojiro Tanaka

¹Department of Mathematics and Computer Science, Interdisciplinary Faculty of Science and Engineering, Shimane University, Matsue, Shimane, 690-8502 Japan. aizawa@cis.shimane-u.ac.jp

IEEE Transactions on Pattern Analysis and Machine Intelligence

|May 16, 2009

Summary

A new constant-time algorithm efficiently finds neighbors in quadtrees (hierarchical data structures). This method significantly reduces computational complexity for quadtree-based algorithms, improving performance in image processing and spatial data analysis.

Related Experiment Videos

Last Updated: Jun 23, 2026

Collecting and Processing Drone-based Remotely Sensed Data for Use in Forest Recovery Monitoring

Collecting and Processing Drone-based Remotely Sensed Data for Use in Forest Recovery Monitoring

Published on: October 24, 2025

Area of Science:

Computer Science
Data Structures
Image Processing

Background:

Quadtrees and linear quadtrees are hierarchical data structures for representing square images.
Finding neighbors of a leaf node is crucial for quadtree algorithms.
Existing quadtree neighbor-finding methods have a worst-case time complexity of O(r).

Purpose of the Study:

To propose a novel algorithm for finding neighbors of a leaf node in a quadtree.
To achieve a worst-case computational time complexity of O(1) for neighbor finding.
To eliminate the need for additional existence checks, simplifying the process.

Main Methods:

Development of a new O(1) worst-case time complexity algorithm for neighbor finding in quadtrees.
The algorithm directly calculates neighbor locations without requiring subsequent existence verification.
Focus on leaf node neighbor identification within the quadtree structure.

Main Results:

The proposed algorithm finds neighbors in constant O(1) time, regardless of quadtree resolution (r).
The algorithm inherently handles neighbor existence without explicit checks.
Significant reduction in computational complexity for quadtree-based operations.

Conclusions:

The new algorithm offers a substantial improvement over existing methods for finding neighbors in quadtrees.
Its constant-time performance and simplified approach enhance the efficiency of numerous quadtree applications.
This advancement is expected to benefit various fields utilizing hierarchical spatial data structures.