Efficient Algorithms for the All Nearest Neighbor and Closest Pair Problems on the Linear Array with a Reconfigurable Pipelined Bus System

• Authors: Yuh-Rau Wang;Shi-Jinn Horng;Chin-Hsiung Wu
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 2005

In this paper, we present two O(1) time algorithms for solving the 2D all nearest neighbor (2D_ANN) problem, the 2D closest pair (2D_CP) problem, the 3D all nearest neighbor (3D_ANN) problem and the 3D closest pair (3D_CP) problem of n points on the linear array with a reconfigurable pipelined bus system (LARPBS) from the computational geometry perspective. The first O(1) time algorithm, which invokes the ANN properties (introduced in this paper) only once, can solve the 2D_ANN and 2D_CP problems of n points on an LARPBS of size {\frac{1}{2}}n^{{\frac{5}{3}}+\epsilon}, and the 3D_ANN and 3D_CP problems of n points on an LARPBS of size {\frac{1}{2}}n^{{\frac{7}{4}}+\epsilon}, where 0