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A new proof of static optimality for splay tree

Thatchaphol Saranurak
KTH, Royal Institute of Technology
AG1 Mittagsseminar (own work)
AG 1, AG 2, AG 3, AG 4, AG 5, RG1, SWS, MMCI  
AG Audience
English

Date, Time and Location

Thursday, 14 April 2016
13:00
30 Minutes
E1 4
024
Saarbrücken

Abstract

Splay tree [Sleator Tarjan JACM'85] is a classic dynamic binary search tree algorithm that can rearrange a tree after each access. It has been conjectured in the same paper that the cost of splay tree for accessing any access sequence is at most constant factor away from the cost of every BST algorithm even if such algorithm knows the whole sequence in advanced. This conjecture is called “dynamic optimality” which is considered one of the most fundamental open problems about data structures, and is still wide open.


It has been proven that splay tree satisfies several other weaker properties. One important example of these properties is called “static optimality” which states that the cost of splay tree for accessing any access sequence is at most constant factor away from the cost of every static BST algorithm, that cannot rearrange a tree after each access. The original proof [Sleator Tarjan JACM'85] is via a so-called “sum-of-logs” potential function. Though the proof is very elegant and easy to verify, it is not clear why it works and how to come up with such potential function.

We give an arguably simpler proof of static optimality for splay tree via a new potential function called MinDepth. It is straightforward and combinatorial. We believe that this proof is a nice material for teaching in data structure classes.

Contact

Parinya Chalermsook
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Parinya Chalermsook, 04/13/2016 20:50
Parinya Chalermsook, 03/30/2016 20:25 -- Created document.