An O(loglog n)-Competitive Binary Search Tree with Optimal Worst-Case Access Times

TL;DR

This paper introduces the zipper tree, a binary search tree that achieves both optimal worst-case access times and near-optimal amortized performance, advancing the efficiency of online data structures.

Contribution

The zipper tree is the first online binary search tree to guarantee both $O( ext{log} ext{log} n)$ competitiveness and $O( ext{log} n)$ worst-case access time.

Findings

Achieves $O( ext{log} ext{log} n)$ competitiveness.

Performs each access in $O( ext{log} n)$ worst-case time.

Demonstrates simultaneous optimal worst-case and near-optimal amortized performance.

Abstract

We present the zipper tree, an $O(\log \log n)$-competitive online binary search tree that performs each access in $O(\log n)$ worst-case time. This shows that for binary search trees, optimal worst-case access time and near-optimal amortized access time can be guaranteed simultaneously.