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What and Who
Title:A new proof of static optimality for splay tree
Speaker:Thatchaphol Saranurak
coming from:KTH, Royal Institute of Technology
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
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Level:AG Audience
Language:English
Date, Time and Location
Date:Thursday, 14 April 2016
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
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
Name(s):Parinya Chalermsook
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Created by:Parinya Chalermsook, 03/30/2016 08:25 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Parinya Chalermsook, 04/13/2016 08:50 PM
  • Parinya Chalermsook, 03/30/2016 08:25 PM -- Created document.