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February, 1995 On the Markov Chain for the Move-to-Root Rule for Binary Search Trees
Robert P. Dobrow, James Allen Fill
Ann. Appl. Probab. 5(1): 1-19 (February, 1995). DOI: 10.1214/aoap/1177004824


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.


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Robert P. Dobrow. James Allen Fill. "On the Markov Chain for the Move-to-Root Rule for Binary Search Trees." Ann. Appl. Probab. 5 (1) 1 - 19, February, 1995.


Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0822.60058
MathSciNet: MR1325037
Digital Object Identifier: 10.1214/aoap/1177004824

Primary: 60J10
Secondary: 68P05 , 68P10

Keywords: Binary search trees , Eigenvalues , lumping , Markov chains , Move-to-front rule , move-to-root rule , self-organizing search , simple exchange

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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