No abstract

This paper propose an extended form of Red Black trees. It presents a new explicit balancing algorithm called Red Green Black trees. This structure tolerates some degree of imbalance that allows a decrease of the number of rebalancing relaxing the update operations. Through the use of three color nodes, the structure tolerates series of two nodes between Black nodes and defines a less balanced tree. It is interesting because the imbalance doesn't affect the update time and save the same level of performances of Red Black trees of O(log(n)). In fact, Red Green Black trees can provide better performances in environment where the restructuring is most frequent with Red Black trees.

We introduce the Partitioned Trees, a form of Partitioned Binary Search Tree parameterized to represent both Red-Black trees and a family of partially balanced Binary Search Trees. Partitioned Tree is interesting not only because it provides the same time and space complexity as Balanced Binary Search trees O(logn), but also because it’s simple to implement, easily understandable, and highly adaptable in different fields where rebalancing is costly. We outline the various maintenance operations and insertion and deletion algorithms employed by the proposed data structure. Additionally, we conduct an in-depth analysis on the worst-case height of Partitioned Trees followed by a comparison of Partitioned Trees and Red-Black Trees. Our simulations confirm that Partitioned Trees exhibit superior performance compared to Red-Black Trees.