Universal Asymptotics for Random Tries and PATRICIA Trees

Abstract. We 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. Keywords and phrases. Trie, patricia tree, probabilistic analysis, law of large numbers, concentration inequality, height of a tree. CR Categories: 3.74, 5.25, 5.5. 1991 Mathematics Subject Classifications: 60D05, 68U05. Author' address: School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2K6. The author' research was spon...

• Type: Journal
• Year: 2005
• Where: ALGORITHMICA
• Authors: Luc Devroye
• Keywords: ALGORITHMICA 2005, Patricia Tree, Random Patricia Trees, Random Structures