Manipulation of Sets of Numbers.

A new approach to the manipulation of sets of numbers is studied. A new type of tree is introduced which permits a convenient representation of sets of numbers yielding efficient algorithms for operations such as searching, inserting or deleting numbers in a set. Compared to proposals such as AVL-trees, trees with bounded balance and symmetric B-trees, the restructuring procedures are intuitively more obvious. Compared to proposals using nonbinary trees such as B-trees and 2-3 trees, the binary nature of the trees proposed yields simpler algorithms. For a general study of algorithms for the manipulation of sets of numbers, operations on sets with repetitions are proposed. Within a general framework for measuring various algorithms the usefulness of the new types of tree is established.