# New Results for the Minimum Weight Triangulation Problem

1992) New Results for the Minimum Weight Triangulation Problem. Technical Report TR-92-30, Computer Science, Virginia Polytechnic Institute and State University. (

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## Abstract

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(n3) time and that never does worse than the greedy triangulation. We investigate issues of local optimality pertaining to known triangulation algorithms and suggest an interesting new approach to studying triangulation algorithms. We restate the minimum weight triangulation problem as a graph problem and show the NP-hardness of a closely related graph problem. Finally, we show that the constrained problem of computing the minimum weight triangulation, given a set of points in a plane and enough edges to form a triangulation, is NP-hard. These results are an advance towards a proof that the minimum weight triangulation problem is NP-hard.

Item Type: | Departmental Technical Report |
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Subjects: | Computer Science > Historical Collection(Till Dec 2001) |

ID Code: | 310 |

Deposited By: | User autouser |

Deposited On: | 05 December 2001 |