Engineering Top-Down Weight-Balanced Trees

TL;DR

This paper analyzes and engineers top-down weight-balanced trees, revealing their superior performance and providing insights into parameter selection, including counterintuitive benefits of choosing parameters outside traditional correctness bounds.

Contribution

It offers an in-depth analysis and engineering of top-down weight-balanced trees, a less-studied variant, demonstrating their advantages and exploring parameter choices.

Findings

Top-down weight-balanced trees outperform bottom-up variants in practical performance.

Choosing parameters outside traditional bounds can be beneficial for balancing efficiency.

Insights into parameter selection improve the design of weight-balanced trees.

Abstract

Weight-balanced trees are a popular form of self-balancing binary search trees. Their popularity is due to desirable guarantees, for example regarding the required work to balance annotated trees. While usual weight-balanced trees perform their balancing operations in a bottom-up fashion after a modification to the tree is completed, there exists a top-down variant which performs these balancing operations during descend. This variant has so far received only little attention. We provide an in-depth analysis and engineering of these top-down weight-balanced trees, demonstrating their superior performance. We also gaining insights into how the balancing parameters necessary for a weight-balanced tree should be chosen - with the surprising observation that it is often beneficial to choose parameters which are not feasible in the sense of the correctness proofs for the rebalancing algorithm.