Continuous-time digital search tree and a border aggregation model

Abstract

We consider the continuous-time version of the random digital search tree, and construct a coupling with a border aggregation model as studied in Thacker and Volkov (Ann. Appl. Probab. 28 (2018) 1604–1633), showing a relation between the height of the tree and the time required for aggregation. This relation carries over to the corresponding discrete-time models. As a consequence we find a very precise asymptotic result for the time to aggregation, using recent results by Drmota et al. (Random Structures Algorithms 58 (2021) 430–467) for the digital search tree.