An efficient way to manage ranges of data with Wise Red-Black Trees

TL;DR

This paper introduces Wise Red-Black Trees, an optimized data structure for efficiently managing range operations in ordered sets, improving average and worst-case performance without increasing space usage.

Contribution

It presents a novel augmented Red-Black Tree variant that enhances range operation efficiency and reduces constants in worst-case scenarios.

Findings

Improved average-case operation times

Reduced multiplicative constants in worst-case performance

Maintains space complexity of traditional Red-Black Trees

Abstract

This paper describes the most efficient way to manage operations on ranges of elements within an ordered set. The goal is to improve existing solutions, by optimizing the average-case time complexity and getting rid of heavy multiplicative constants in the worst-case, without sacrificing space complexity. This is a high-impact operation in practical applications, performed by introducing a new data structure called Wise Red-Black Tree, an augmented version of the Red-Black Tree.