Digital access to comparison-based tree data structures and algorithms

Abstract

This paper presents a simple method to build tree data structures which achieve just O(log N) visited nodes and O(D) compared digits (bits or bytes) per search or update, where N is the number of keys and D is the length of the keys, irrespectively of the order of the updates and of the digital representation of the keys. The additional space required by the method is asymptotically dismissable compared to the space of keys and pointers, and is easily updated on line. The method applies to fixed-length base-2 keys and to variable-length string keys as well, and permits to save space for common prefixes. The same ideas can be applied to the sorting problem, achieving algorithms with the best properties of quicksort/mergesort and radixsort together.