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A Simple Balanced Search Tree With O(1) WorstCase Update Time
"... In this paper we show how a slight modification of (a; b)trees allows us to perform member and neighbor queries in O(log n) time and updates in O(1) worstcase time (once the position of the inserted or deleted key is known). Our data structure is quite natural and much simpler than previous worst ..."
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In this paper we show how a slight modification of (a; b)trees allows us to perform member and neighbor queries in O(log n) time and updates in O(1) worstcase time (once the position of the inserted or deleted key is known). Our data structure is quite natural and much simpler than previous worstcase optimal solutions. It is based on two techniques : 1) bucketing, i.e. storing an ordered list of 2 log n keys in each leaf of an (a; b) tree, and 2) lazy splitting, i.e. postponing necessary splits of big nodes until we have time to handle them. It can also be used as a finger tree with O(log n) worstcase update time. 1 . Introduction One of the most common (and most important) data structures used in efficient algorithms is the balanced search tree. Hence there exists a great variety of them in literature. Basically, they all store a set of n keys such that location, insertion and deletion of keys can be accomplished in O(log n) worstcase time. In general, updates (insertions or ...
An Overview over RedBlack and Finger Trees
, 1992
"... 2 1 1 Figure 1: A redblack 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 redblack trees, but othe ..."
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2 1 1 Figure 1: A redblack 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 redblack 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 redblack 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 redblack tree is a full binary tree in which each node is assigned a color, either red or black. The leaves are called