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

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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

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

First available in Project Euclid: 19 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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.

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