We present the zipper tree, an O(loglogn)-competitive online binary search tree that performs each access in O(logn) 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.
@article{arxiv.1003.0139,
title = {An O(loglog n)-Competitive Binary Search Tree with Optimal Worst-Case Access Times},
author = {Prosenjit Bose and Karim Douïeb and Vida Dujmovic and Rolf Fagerberg},
journal= {arXiv preprint arXiv:1003.0139},
year = {2015}
}