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