In pursuit of the dynamic optimality conjecture

TL;DR

This paper surveys the progress on the dynamic optimality conjecture for splay trees and introduces a binary search tree algorithm that is dynamically optimal if such an optimal algorithm exists.

Contribution

It provides a comprehensive survey of the nearly thirty-year effort on the conjecture and proposes a new algorithm that is conditionally dynamically optimal.

Findings

Survey of thirty years of research on the conjecture

Introduction of a new binary search tree algorithm

Conditional proof of dynamic optimality if any exists

Abstract

In 1985, Sleator and Tarjan introduced the splay tree, a self-adjusting binary search tree algorithm. Splay trees were conjectured to perform within a constant factor as any offline rotation-based search tree algorithm on every sufficiently long sequence---any binary search tree algorithm that has this property is said to be dynamically optimal. However, currently neither splay trees nor any other tree algorithm is known to be dynamically optimal. Here we survey the progress that has been made in the almost thirty years since the conjecture was first formulated, and present a binary search tree algorithm that is dynamically optimal if any binary search tree algorithm is dynamically optimal.