Red-Black Trees with Constant Update Time

TL;DR

This paper introduces a modified red-black tree structure that achieves constant worst-case update time, simplifies implementation, and provides a novel deletion procedure without global rebuilding.

Contribution

It presents a new red-black tree variant with constant update time and a unique deletion method, improving simplicity and theoretical guarantees.

Findings

Achieves O(1) worst-case update time after position known

Provides a simple, implementable red-black tree variant

Introduces a deletion procedure without global rebuilding

Abstract

We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the red-black trees while guaranteeing that the height remains logarithmic with respect to the number of nodes. Compared to the other search trees with constant update time, our tree is the first to provide a tailored deletion procedure without using the global rebuilding technique. In addition, our structure is very simple to implement and allows for a simpler proof of correctness than those alternative trees.