Approximate Axis-Aligned Nearest Neighbor

The nearest neighbor problem is a fundamental challenge in computer and data science, essential for tasks ranging from classification to clustering and beyond. As data dimensionality increases, traditional methods like brute-force search and structure-oriented algorithms such as k-D trees become computationally infeasible. This paper introduces the Approximate Axis-Aligned Nearest Neighbor (AAANN) algorithm, designed to efficiently address the nearest neighbor problem in both low and high-dimensional spaces. The algorithm leverages axis-aligned projections to achieve superior performance for dimensions less than 10, outperforming traditional methods. For higher dimensions, the Taxicab algorithm is recommended due to its robustness and efficiency. Extensive experimental evaluations demonstrate the effectiveness of AAANN, with potential applications in classification searches, ray-tracing, path planning, collision detection, and n-body simulations. The AAANN algorithm represents a significant advancement in the field, offering a scalable and efficient solution to the nearest neighbor problem across a wide range of dimensions.