GFBツリーとツリー不均衡指数
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
まとめ
亜木のサイズから派生した新しい木の不均衡指標を導入し, 完全と底から貪欲な (GFB) 木はそれらを最小限に抑え, カタツムリの木はそれらを最大限にします. GFBツリーは,s形統計のユニークな最小化器です.
科学分野:
- 系統遺伝学
- コンピュータ科学
- グラフ理論
背景:
- 樹木のバランスは 系統遺伝学とコンピュータサイエンスの分野において 極めて重要です
- 根付いたバイナリーツリーをランク付けするために25以上のバランス/不均衡インデックスがあります.
- サブツリーサイズに基づく測定は,木の構造を定量化するために一般的です.
研究 の 目的:
- 樹木の不均衡指数の新しいファミリーを導入する.
- これらのインデックスの最小化と最大化を特定します.
- 下から貪欲な (GFB) 木の特徴を特定し,特定の統計を分析する.
主な方法:
- 穴と単調性を満たす子木のサイズに基づく測定値を調べた.
- 完全な木と底から貪欲な (GFB) 木を分析した.
- 特定のツリー分布の下の s 形と Q 形の統計のためのアシンプトティックな境界を導いた.
主要な成果:
- 完全な/GFB樹は,幅広い不均衡指標を最小限に抑え,毛虫樹はそれらを最大限に抑えます.
- GFBツリーは,s形統計のユニークな最小化器です.
- GFB樹と完全な樹の間の同等性を確立しました.
結論:
- この研究は,新しい不均衡指標の無限の家族を生み出します.
- GFB樹の新しい特徴を提示しています.
- 異なる分布下での木の不均衡統計の振る舞いについての洞察を提供します.
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