Minimum-weight triangulation is NP-hard
计算几何
2010-04-19 v3 计算复杂性
摘要
A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.
引用
@article{arxiv.cs/0601002,
title = {Minimum-weight triangulation is NP-hard},
author = {Wolfgang Mulzer and Guenter Rote},
journal= {arXiv preprint arXiv:cs/0601002},
year = {2010}
}
备注
45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the exposition