New results for the minimum weight triangulation problem
 L. S. Heath,
 S. V. Pemmaraju
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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 polynomialtime algorithm is known to find a triangulation of minimum weight, nor is the minimum weight triangulation problem known to be NPhard. This paper proposes a new heuristic algorithm that triangulates a set ofn points inO(n ^{ 3) } 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 NPhard, two generalizations that are quite close to the minimum weight triangulation problem are shown to be NPhard.
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 Title
 New results for the minimum weight triangulation problem
 Journal

Algorithmica
Volume 12, Issue 6 , pp 533552
 Cover Date
 19941201
 DOI
 10.1007/BF01188718
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Minimum weight triangulation
 Greedy triangulation
 Delaunay triangulation
 Minimum spanning tree
 NPHardness
 Industry Sectors
 Authors

 L. S. Heath ^{(1)}
 S. V. Pemmaraju ^{(2)}
 Author Affiliations

 1. Department of Computer Science, Virginia Polytechnic Institute and State University, 24061, Blacksburg, IA, USA
 2. Department of Computer Science, University of Iowa, 52242, Iowa City, IA, USA