对称数字搜索树的节点分布：集中性质
概率论
2020-09-30 v5
摘要
我们对随机对称数字搜索树的分布给出了详细的渐近分析，这些分布与此类树中随机查询的搜索复杂度性能密切相关。尽管期望分布已被分析数十年，但方差的分析被证明非常困难且富有挑战性，需要结合多种不同的解析技术，包括 Mellin 变换和 Laplace 变换、解析去泊松化以及 Laplace 卷积。我们的结果意味着在均值趋于无穷的范围内分布是集中的。此外，我们还获得了高度和饱和层分布的两点集中性。
引用
@article{arxiv.1711.06941,
title = {Node Profiles of Symmetric Digital Search Trees: Concentration Properties},
author = {Michael Drmota and Michael Fuchs and Hsien-Kuei Hwang and Ralph Neininger},
journal= {arXiv preprint arXiv:1711.06941},
year = {2020}
}
备注
The central limit theorem was removed from this version (and moved to a follow-up paper) since the proof in the previous versions was incomplete. Also, the word "Concentration Properties" was added to the title since this part now entirely focuses on such results