Digital Access to Comparison-Based Tree Data Structures and Algorithms

This paper presents a simple method of building tree data structures, which only requires visiting O(log N) nodes and comparing O(D) digits per search or update, where N is the number of keys and D is the length of the keys. These bounds hold independently of the order of the updates and of the digits of the keys. The additional space required by the method is asymptotically dismissable when compared to the space used by the keys and pointers. The proposed method applies either to fixed-length base-2 keys or to variable-length string keys and permits saving space for common prefixes. The same ideas can be applied to achieve algorithms that have the best bounds of quicksort or of mergesort and radixsort together.