The height of depth‐weighted random recursive trees. Issue 3 (12th January 2020) - Leckey, Kevin; Mitsche, Dieter; Wormald, Nick
Abstract : In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex v . In this model, the probability of choosing v depends on its depth in the tree. In particular, we assume that there is a function f such that if v has depth k then its probability of being chosen is proportional to f ( k ) . We consider the expected value of the diameter of this model as determined by f, and for various increasing f we find expectations that range from polylogarithmic to linear.