Improving the Red-Black tree delete algorithm

Abstract

Today, Red-Black trees are becoming a popular data structure typically used to implement dictionaries, associative arrays, symbol tables within some compilers (C++, Java …) and many other systems. In this paper, we present an improvement of the delete algorithm of this kind of binary search tree. The proposed algorithm is very promising since it colors differently the tree while reducing color changes by a factor of about 29%. Moreover, the maintenance operations re-establishing Red-Black tree balance properties are reduced by a factor of about 11%. As a consequence, the proposed algorithm saves about 4 % on running time when insert and delete operations are used together while conserving search performance of the standard algorithm.

A symbolic-arithmetic for teaching double-black node removal in red-black trees

“…Whereas, the insertion operation of a new node in a RB tree is the simpler of two hard problems: With the harder being the deletion of a black node or the replacement node [6] and the subsequent rebalancing of the tree. In order to address the removal of DB node, Zegour [24] used formalized statements in the description of nodes' color, recoloring and tree balancing without simplifying the challenges in students' learning of the DB removal algorithm. In [6] a parityseeking delete algorithm was introduced with the goal similar to the aim of our paper: to introduce a pedagogically sound and easy way to understand the algorithm for RB tree deletion algorithm.…”

Partitioned Trees

“…Others (Boyar and Larsen, 1994;Park and Park, 2001;Larsen, 2002;Besa and Eterovic, 2013;Howard and Walpole, 2014) sought to decouple updates from rebalancing, enabling a greater degree of concurrency and postponed processing. Additionally, (Zegour, 2022b) proposed an improvement to the delete algorithm of RB Trees that reduces color changes by roughly 29% and maintenance operations by about 11%. Combining this algorithm with insert and delete operations results in a 4% reduction in running time, while preserving the search performance of the standard algorithm.…”