On the number of string lookups in BSTs (and related algorithms) with digital access

Binary search trees and quicksort are examples of comparison-based data structure and algorithm respectively. Comparison-based data structures and algorithms can be can be augmented so that no redundant character comparisons are made. Unnoticed, this approach also avoids looking up the string in some nodes. This paper haracterizes analytically the number of string lookups in so-augmented BSTs, quicksort and quickselect. Besides, we also characterize a variant proposed in this paper to reduce further the number of string lookups.Postprint (published version

Universal Asymptotics for Random Tries and Patricia Trees

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 Z_n of these random structures are universally stable in the sense that Z_n/E{Z_n} tends to one probability. This occurs, for example, when Z_n 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