2 1 1 Figure 1: A red-black tree. The darkened nodes are black nodes. The external nodes are denoted by squares. Shown with each node is its rank. Wyk give another, simpler, implementation of finger trees. They describe a finger data structure which is a modification of red-black trees, but other forms of balanced trees could be used as a basis for the structure. The two problems presented in Chapters 3 and 4 rely on the use of redblack and finger trees respectively. In this chapter we give a fairly complete overview of red-black trees, of the finger trees introduced by Tarjan and Van Wyk, and of a variant of these which we use in Chapter 4. The material here is intended to be comprehensive and useful as an introduction to these two types of data structures. Re - ack rees A red-black tree is a full binary tree in which each node is assigned a color, either red or black. The leaves are called