# In Pursuit of the Dynamic Optimality Conjecture

@article{Iacono2013InPO, title={In Pursuit of the Dynamic Optimality Conjecture}, author={John Iacono}, journal={ArXiv}, year={2013}, volume={abs/1306.0207} }

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…

## 23 Citations

Competitive Dynamic Bsts .. Two Cost Models

- Computer Science

This work describes a conceptually simple but computationally expensive dynamic binary search tree that is-competitive if the cost of rotations is ignored, and proposes a deterministic weakly bounded skip list that is dynamically optimal.

New Paths from Splay to Dynamic Optimality

- Computer ScienceArXiv
- 2019

This work attempts to lay the foundations for a proof of the dynamic optimality conjecture, which is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches.

Better Analysis of GREEDY Binary Search Tree on Decomposable Sequences

- Computer ScienceTheor. Comput. Sci.
- 2019

A Foundation for Proving Splay is Dynamically Optimal

- Computer Science
- 2019

It is proved that a lower bound on optimal execution cost is approximately monotone and details how to adapt this proof from the lower bound to Splay, and how to overcome the remaining barriers to establishing dynamic optimality.

Pinning Down the Strong Wilber 1 Bound for Binary Search Trees

- Computer ScienceAPPROX-RANDOM
- 2020

It is shown that the gap between the stronger WB-1 bound and $OPT$ may be as large as $\Omega(\log\log n/\log\ log n)$.

Binary search trees, rectangles and patterns

- Computer Science
- 2016

Splay, a popular BST algorithm that has several proven efficiency properties, is generalized, and a set of sufficient (and, in a limited sense, necessary) criteria that guarantee the efficient behavior of a BST algorithm is defined.

Greedy Is an Almost Optimal Deque

- Computer ScienceWADS
- 2015

This paper extends the geometric binary search tree model of Demaine, Harmon, Iacono, Kane, and Pǎtrascu (DHIKP) to accommodate for insertions and deletions and studies the online Greedy BST algorithm introduced by DHIKP.

Splay trees on trees

- Computer ScienceSODA
- 2022

It is shown that a $(1 + \frac{1}{t})-approximation of an optimal size-$n STT for a given search distribution can be computed in time, and a broad family of STTs with linear rotation-distance is identified, allowing the generalization of Splay trees to the STT setting.

Competitive Online Search Trees on Trees

- Computer ScienceSODA
- 2020

This work uses a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree, and describes an online $O(\log \log n)-competitive search tree data structure in this model, matching the best known competitive ratio of binary search trees.

What Does Dynamic Optimality Mean in External Memory?

- Computer ScienceITCS
- 2022

This paper revisits the question of how dynamic optimality should be deﬁned in external memory and gives an elegant data structure, called the Belga B-tree, that is within an O (log log N )-factor of being dynamically optimal over this class of external-memory search trees.

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