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The height of depth‐weighted random recursive trees
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2020-01-12 , DOI: 10.1002/rsa.20901 Kevin Leckey 1 , Dieter Mitsche 2, 3, 4 , Nick Wormald 5
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2020-01-12 , DOI: 10.1002/rsa.20901 Kevin Leckey 1 , Dieter Mitsche 2, 3, 4 , Nick Wormald 5
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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:
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。
更新日期:2020-04-23
中文翻译:
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。