Unbalancing Binary Trees

TL;DR

This paper introduces a new approximate optimization method for binary trees that is faster and more accurate than existing techniques, especially when the searched node is likely within the tree.

Contribution

A novel O(n log n) approximate optimization technique for binary trees that outperforms existing methods in accuracy and applicability.

Findings

Existing methods are about 10% worse than optimal.

New method achieves only 1% deviation from optimal.

Technique is applicable when the searched node is likely in the tree.

Abstract

Assuming Zipf's Law to be accurate, we show that existing techniques for partially optimizing binary trees produce results that are approximately 10% worse than true optimal. We present a new approximate optimization technique that runs in O(n log n) time and produces trees approximately 1% worse than optimal. The running time is comparable to that of the Garsia-Wachs algorithm but the technique can be applied to the more useful case where the node being searched for is expected to be contained in the tree as opposed to outside of it.