GFB树和树不平衡指数
Sean Cleary1, Mareike Fischer2, Katherine St John3
1Department of Mathematics, The City College of New York, New York, 10031, USA.
Bulletin of mathematical biology
|September 5, 2025
概括
我们引入了从子树大小中获得的新树不平衡指数, 显示完整和从底部贪 (GFB) 树最小化它们, 而虫树最大化它们. GFB树是s形统计的唯一最小化器.
科学领域:
- 遗传学
- 计算机科学
- 图形理论
背景情况:
- 在遗传学和计算机科学中树木平衡至关重要.
- 有超过25个平衡/不平衡指数来对根植的二进制树进行排名.
- 基于子树大小的测量是树结构量化的常见方法.
研究的目的:
- 引入一个新的树不平衡指数家族.
- 确定这些指数的最小化和最大化值.
- 描述从底部开始的贪 (GFB) 树,并分析具体的统计数据.
主要方法:
- 研究的基于子树大小的测量满足腔性和单调性.
- 分析完整的树木和从底部 (GFB) 的贪树木.
- 在特定树分布下为s-shape和Q-shape统计学衍生了非对称边界.
主要成果:
- 完整/GFB树最小化了各种不平衡指数;毛虫树最大化了它们.
- GFB树是s形统计的唯一最小化器.
- 确定了GFB树和完整树之间的等价性.
结论:
- 这项研究产生了一系列新的失衡指数.
- 提供了GFB树的新特征.
- 提供了不同分布下的树不平衡统计行为的见解.
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