In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex . In this model, the probability of choosing depends on its depth in the tree. In particular, we assume that there is a function such that if has depth then its probability of being chosen is proportional to . We consider the expected value of the diameter of this model as determined by , and for various increasing we find expectations that range from polylogarithmic to linear.

中文翻译：

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深度加权随机递归树的高度

在本文中，我们介绍了一种深度加权随机递归树模型，该模型是通过将新叶子递归连接到现有顶点而创建的。在此模型中，选择的可能性取决于其在树中的深度。特别地，我们假设存在一个函数，使得如果具有深度，则其被选择的概率与成正比。我们认为该模型的直径的期望值由确定，对于各种增长，我们发现期望值范围从对数到线性。