On Dynamic Optimality for Binary Search Trees

TL;DR

This paper advances the understanding of binary search tree algorithms by showing that a well-known greedy algorithm is O(log n)-competitive, moving closer to the long-standing goal of O(1)-competitiveness.

Contribution

The paper proves that the GreedyArb algorithm is O(log n)-competitive, providing progress towards the open problem of O(1)-competitiveness for BSTs.

Findings

GreedyArb is O(log n)-competitive.

Progress towards O(1)-competitiveness for BST algorithms.

Uses geometric view to analyze online BST algorithms.

Abstract

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.