Universal Asymptotics for Random Tries and PATRICIA Trees

AbstractWe consider random tries and random patricia trees constructed from n independent strings of symbols drawn from any distribution on any discrete space. We show that many parameters Zn of these random structures are universally stable in the sense that Zn/E{Zn} tends to one probability. This occurs, for example, when Zn is the height, the size, the depth of the last node added, the number of nodes at a given depth (also called the profile), the search time for a partial match, the stack size, or the number of nodes with k children. These properties are valid without any conditions on the string distributions.

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