A Simple Balanced Search Tree With O(1) Worst-Case Update Time
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@MISC{Fleischer_asimple,
author = {Rudolf Fleischer},
title = {A Simple Balanced Search Tree With O(1) Worst-Case Update Time},
year = {}
}
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Abstract
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) worst-case time (once the position of the inserted or deleted key is known). Our data structure is quite natural and much simpler than previous worst-case 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) worst-case 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) worst-case time. In general, updates (insertions or ...
