  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.
