多边形链在四维空间中不会锁定
计算几何
2007-05-23 v3 离散数学
摘要
我们证明了在所有维度 d>=4 下，每条简单开多边形链和每棵树都可以被拉直，且每条简单闭多边形链都可以被凸化。这些重构可以通过使用关于顶点数呈多项式时间的算法实现，并产生多项式数量的“移动”。这些结果不同于 d=2（其中树可以“锁定”）和 d=3（其中开链和闭链可以锁定）的已知结果。
引用
@article{arxiv.cs/9908005,
title = {Polygonal Chains Cannot Lock in 4D},
author = {Roxana Cocan and Joseph O'Rourke},
journal= {arXiv preprint arXiv:cs/9908005},
year = {2007}
}
备注
Major revision of the Aug. 1999 version, including: Proof extended to show trees cannot lock in 4D; new example of the implementation straightening a chain of n=100 vertices; improved time complexity for chain to O(n^2); fixed several minor technical errors. (Thanks to three referees.) 29 pages; 15 figures. v3: Reference updated