A hashing-oriented nearest neighbor searching scheme

Abstract

This paper presents a hashing-oriented nearest neighbor searching scheme. Given n points in the Euclidean two-dimensional plane, we first construct a Voronoi diagram and record the Voronoi vertices and the Voronoi edges. By passing each Voronoi vertex, we use two perpendicular lines, one is horizontal and the other is vertical, to partition the plane into some rectangular subdivisions. Here, each rectangular subdivision dominates at most two given points. Then we establish two hashing functions corresponding to horizontal slabs and vertical slabs, respectively. By applying the established hashing functions, we can quickly determine the proper rectangular subdivision containing the query point. After that, we compare the distance between the query point and the dominated points to determine the nearest neighbor. The searching time by our scheme is O(1). The preprocessing time and the amount of required storage are O( n 2 + t), respectively, where n is the number of given points and t is the size of the hashing table needed by the established hashing functions.