Algorithmica

, Volume 12, Issue 6, pp 533–552

New results for the minimum weight triangulation problem

  • L. S. Heath
  • S. V. Pemmaraju
Article

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. No polynomial-time algorithm is known to find a triangulation of minimum weight, nor is the minimum weight triangulation problem known to be NP-hard. This paper proposes a new heuristic algorithm that triangulates a set ofn points inO(n3) time and that never produces a triangulation whose weight is greater than that of a greedy triangulation. The algorithm produces an optimal triangulation if the points are the vertices of a convex polygon. Experimental results indicate that this algorithm rarely produces a nonoptimal triangulation and performs much better than a seemingly similar heuristic of Lingas. In the direction of showing the minimum weight triangulation problem is NP-hard, two generalizations that are quite close to the minimum weight triangulation problem are shown to be NP-hard.

Key words

Minimum weight triangulation Greedy triangulation Delaunay triangulation Minimum spanning tree NP-Hardness 

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Copyright information

© Springer-Verlag New York Inc 1994

Authors and Affiliations

  • L. S. Heath
    • 1
  • S. V. Pemmaraju
    • 2
  1. 1.Department of Computer ScienceVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of Computer ScienceUniversity of IowaIowa CityUSA

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