Decreasing Radius K-Nearest Neighbor Search using Mapping-based Indexing Schemes

A decreasing radius k-nearest neighbor search algorithm for the mapping-based indexing schemes is presented. We implement the algorithm in the Pyramid technique and the iMinMax(θ), respectively. The Pyramid technique divides d-dimensional data space into 2d pyramids, and the iMinMax(θ) divides the data points into d partitions. Given a query point q, we initialize the radius of a range query to be the furthest distance of the k candidate nearest neighbors from q in the pyramid (partition) which q is in, then examine the rest of the pyramids (partitions) one by one. After one pyramid (partition) is checked, the radius of the range query decreases or remains the same. We compare the decreasing radius k-nearest neighbor search algorithm with the increasing radius k-nearest neighbor search algorithm using the Pyramid technique and the iMinMax(θ). Moreover, the decreasing radius k-nearest neighbor search performance of these two mapping-based indexing schemes is compared to the BBD-tree, the R∗-tree and naive search. Experimental results show that our decreasing radius k-nearest neighbor search algorithm for the mapping-based indexing schemes is efficient when d ≤ log2 n.