A Fast Algorithm for k -Nearest Neighbor Problem on a Reconfigurable Mesh Computer

Abstract

Given a set S of m points stored on a reconfigurable mesh computer of size n×n, one point per processing element (PE). In this paper we present a parallel method for solving the k-Nearest Neighbor problem (k-NN). This method permits each point of S to know its k-NN (0<k<m). The corresponding algorithm requires that each PE must have 2k registers where it stores the (x,y) coordinates of its k-NN in a given order. This algorithm has a complexity of O(log h+k2) times, where h is a maximal number of points within a row of the mesh. This complexity is reduced to O(k2) times, using an appropriate procedure which demonstrates the power of the reconfiguration operations carried out by the processors, and the polymorphic properties of the mesh.