A Heuristic Algorithm for Finding the Closest Trio of 3-Colored Points from a Given Set of 3-Colored Points on Plane

Abstract

The problem considering in this paper is as follows: Given n red points, m green points and p blue points on plane, how to find a trio of red-green-blue points such that the distance between them is smallest. This problem could be solved by an exhaustive search algorithm: test all trios of 3 different colored points and find the closest one. However, this algorithm has a big complexity: O(nmp). In this paper, we will present a heuristic algorithm with a better complexity to solve this problem. The heuristic algorithm is based on 2D Voronoi diagram.