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February, 1995 Rates of Convergence for the Move-to-Root Markov Chain for Binary Search Trees
Robert P. Dobrow, James Allen Fill
Ann. Appl. Probab. 5(1): 20-36 (February, 1995). DOI: 10.1214/aoap/1177004825


The move-to-root 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 scheme (also known as the weighted random-to-top card shuffle or Tsetlin library) for self-organizing lists. We study convergence of the move-to-root Markov chain to its stationary distribution and show that move-to-root converges two to four times faster than move-to-front for many examples. We also discuss asymptotics for expected search cost. For equal weights, $\operatorname{cn}/\ln n$ steps are necessary and sufficient to drive the maximum relative error to 0.


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Robert P. Dobrow. James Allen Fill. "Rates of Convergence for the Move-to-Root Markov Chain for Binary Search Trees." Ann. Appl. Probab. 5 (1) 20 - 36, February, 1995.


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

zbMATH: 0822.60059
MathSciNet: MR1325038
Digital Object Identifier: 10.1214/aoap/1177004825

Primary: 60J10
Secondary: 68P05 , 68P10

Keywords: Binary search trees , Convergence to stationarity , Markov chains , Move-to-front rule , move-to-root rule , self-organizing search

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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