Abstract

Given a finite set of points in a plane, a triangulation is a maximal set of nonintersecting line segments connecting the points. The weight of a triangulation is the sum of the Euclidean lengths of its line segments. Given a set of points in a plane, the minimum weight triangulation problem is to find a triangulation whose weight is minimum. No polynomial time algorithm is known to solve this problem, and it is also unknown whether the problem is NP-hard. The current best polynomial time approximation algorithm produces a triangulation that can be O(log n) times the weight of the optimal triangulation. We propose an algorithm that triangulates a set P , of n points in a plane in O(n 3 ) time and that never does worse than the greedy triangulation. The algorithm produces an optimal triangulation if the points in P are the vertices of a convex polygon. The algorithm has the flavor of a heuristic proposed by Lingas and an analysis similar to his can be performed for our algorithm also,...

Citations