Kinetic Nearest Neighbor Search in Black-Box Model

Abstract

Proximity problems is a class of important problems which involve estimation of distances between geometric objects. The nearest neighbor search which is a subset of proximity problems, arises in numerous fields of applications, including Pattern Recognition, Statistical classification, Computer vision and etc. In this study, a nearest neighbor search is presented to move points in the plane, while query point is static. The proposed method works in the black-box KDS model, in which the points location received at regular time steps while at the same time, an upper bound dmax is known on the maximum displacement of any point at each time step. In this paper, a new algorithm is presented for kinetic nearest neighbor search problem in the black-box model, under assumptions on the distribution of the moving point set P. It has been shown how the kinetic nearest neighbor will be updated at each time step in O(k∆k logn) amortized time, where ∆k is the k-spread of a point set P. Key words: Computational Geometry, Black Box Model, Kinetic, Nearest Neighbor.