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November, 1993 Optimality of Move-to-Front for Self-Organizing Data Structures with Locality of References
Philippe Chassaing
Ann. Appl. Probab. 3(4): 1219-1240 (November, 1993). DOI: 10.1214/aoap/1177005280


In papers about self-organizing data structures, it is often mentioned that the assumption of independence of successive requests of keys should be relaxed and that the dependence should assume the form of a locality phenomenon. In this setting, the move-to-front rule is considered to be of interest, but no optimality result concerning this rule has yet appeared. In this paper we assume that the sequence of required keys is a Markov chain with a transition kernel $P$ and we consider the class $\mathscr{F}^\ast$ of stochastic matrices $P$ such that move-to-front is optimal among on-line rules, with respect to the stationary search cost. We give properties of $\mathscr{F}^\ast$ that bear out the usual explanation of optimality of move-to-front by a locality phenomenon exhibited by the sequence of required keys. We explicitly produce a large subclass of $\mathscr{F}^\ast$, while showing that in some cases move-to-front is optimal with respect to the speed of convergence toward stationary search cost.


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Philippe Chassaing. "Optimality of Move-to-Front for Self-Organizing Data Structures with Locality of References." Ann. Appl. Probab. 3 (4) 1219 - 1240, November, 1993.


Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0799.68052
MathSciNet: MR1241042
Digital Object Identifier: 10.1214/aoap/1177005280

Primary: 68P05
Secondary: 60J10 , 90C40

Keywords: Bellman optimality condition , Controlled Markov chain , locality , self-organizing data structure , sequential search

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 4 • November, 1993
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