Efficient Computation of the K Nearest Neighbors Query Using Incremental Radius on a k²-tree

Proximity searches within metric spaces are critical for numerous real world applications, including pattern recognition, multimedia information retrieval, and spatial data analysis, among others. With the exponential increase in data volume, the demand for memory efficient structures to store and process information has become increasingly important. In this paper, we present an alternative algorithm for efficient computation of the K-nearest neighbors (KNN) query using the $k^{2}$ -tree compact data structure, using the incremental radius technique. This approach offers an alternative to the existing algorithm that utilizes a priority queue over $k^{2}$ -trees. Through both theoretical and experimental analysis, we demonstrate that our proposed algorithm is up to 2 times faster compared to the priority queue based solution, while also providing substantial improvements in memory efficiency.