The Annals of Applied Probability

On the Markov Chain for the Move-to-Root Rule for Binary Search Trees

Robert P. Dobrow and James Allen Fill

Full-text: Open access

Abstract

The move-to-root (MTR) heuristic is a self-organizing rule that attempts to keep a binary search tree in near-optimal form. It is a tree analogue of the move-to-front (MTF) scheme for self-organizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be derived by lumping the MTF chain and give exact formulas for the transition probabilities and stationary distribution for MTR. We also derive the eigenvalues and their multiplicities for MTR.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 1 (1995), 1-19.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004824

Digital Object Identifier
doi:10.1214/aoap/1177004824

Mathematical Reviews number (MathSciNet)
MR1325037

Zentralblatt MATH identifier
0822.60058

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68P10: Searching and sorting 68P05: Data structures

Keywords
Markov chains self-organizing search binary search trees move-to-root rule lumping eigenvalues simple exchange move-to-front rule

Citation

Dobrow, Robert P.; Fill, James Allen. On the Markov Chain for the Move-to-Root Rule for Binary Search Trees. Ann. Appl. Probab. 5 (1995), no. 1, 1--19. doi:10.1214/aoap/1177004824. https://projecteuclid.org/euclid.aoap/1177004824


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