剥离序列的剥离序列
Adrian Dumitrescu1, Géza Tóth2
1Algoresearch L.L.C., Milwaukee, WI USA.
概括
本研究探讨了从一组中顺序删除点的最小数量的方法,同时始终从凸的船体中删除一个点. 显示的最小路径数大致在O(n^2) 和O(n^3) 之间.
科学领域:
- 计算几何学的计算几何学
- 组合学是一种组合学.
- 几何算法的几何算法
背景情况:
- 凸船体算法是计算几何学的基础.
- 了解点移除过程对于分析几何结构至关重要.
- 处理几何物体的方法的数量可以揭示潜在的组合性质.
研究的目的:
- 确定从总体位置的集合中顺序移除点的最小方法数.
- 分析凸船体剥离过程的组合复杂性.
- 为了确定有效的点移除序列的最小数量的边界.
主要方法:
- 调查点设置在2D平面中的一般位置.
- 分析了从剩余集合的凸体船体中代删除点的过程.
- 根据几何配置推导出组合式和边界.
主要成果:
- 当点处于凸起的位置时,会发生最大的路数,结果是n! 序列. 序列. 这些序列.
- 对于n个点的最小路径数被确定为大约在O(n^2) 和O(n^3) 之间.
- 路径的数量高度依赖于点的特定几何排列.
结论:
- 凸船体剥离序列的最小数量提供了一个测量点集的"非凸性".
- 这项研究有助于理解几何算法的组合格局.
- 导出的边界提供了对几何处理任务的效率和复杂性的见解.
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