Does there exist O(1)-competitive (self-adjusting) binary search tree (BST) algorithms? This is a well-studied problem. A simple offline BST algorithm GreedyFuture was proposed independently by Lucas and Munro, and they conjectured it to be O(1)-competitive. Recently, Demaine et al. gave a geometric view of the BST problem. This view allowed them to give an online algorithm GreedyArb with the same cost as GreedyFuture. However, no o(n)-competitive ratio was known for GreedyArb. In this paper we make progress towards proving O(1)-competitive ratio for GreedyArb by showing that it is O(\log n)-competitive.
Cite
@article{arxiv.1102.4523,
title = {On Dynamic Optimality for Binary Search Trees},
author = {Navin Goyal and Manoj Gupta},
journal= {arXiv preprint arXiv:1102.4523},
year = {2011}
}