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

Nguyen N. T., Duong A. D.

Fundamenta Informaticae

2014

Vol. 130, nr 2

219--229

We consider the following problem: Given n red points, m green points and p blue points on a plane, 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 trio. However, this algorithm has the complexity of O(N3), N = max(n, p, q). In our previous research, we already showed a heuristic algorithm with a good complexity to solve this problem based on 2D Voronoi diagram. In this paper, we introduce a better heuristic algorithm for solving this problem. This new heuristic algorithm has the same complexity but it performs much better than the old one.

A characterization of strict local minimizers of order one for static minmax problems in the parametric constraint case

Taha A. W. A.

Journal of Applied Analysis

2000

Vol. 6, nr 1

139-148

We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.