We are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing trees. These families are typical representatives of tree models with a small depth. Once a tree of size $n$ is compacted by keeping only one occurrence of all fringe subtrees appearing in the tree the resulting graph contains only $O(n / \ln n)$ nodes. This result must be compared to classical results of compaction in the families of simply generated trees, where the analogous result states that the compacted structure is of size of order $n / \sqrt{\ln n}$. The result about the plane binary increasing trees has already been proved, but we propose a new and generic approach to get the result. Finally, an experimental study is presented, based on a prototype implementation of compacted binary search trees that are modeled by plane binary increasing trees.

翻译：我们感兴趣的是对两个古典树系的缩压比率进行定量分析:循环树和平面的二进制树。这些家庭是树型的典型代表,其深度小。一旦一棵大小为$n的树被压缩,只保留了树上所有边缘亚树的一例,所产生的图只包含$O(n / $n n) 的节点。这一结果必须与简单产生的树系的缩压的典型结果相比较,类似结果显示,缩压结构的大小为$/\ sqrt\ n}美元。平面二进制树的结果已经得到证明,但我们提出了取得结果的新的通用方法。最后,根据用平面双进树建模的缩压的两进制搜索树的原型进行了一项实验性研究。