## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 3, Number 4 (1993), 1219-1240.

### Optimality of Move-to-Front for Self-Organizing Data Structures with Locality of References

#### Abstract

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.

#### Article information

**Source**

Ann. Appl. Probab., Volume 3, Number 4 (1993), 1219-1240.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177005280

**Digital Object Identifier**

doi:10.1214/aoap/1177005280

**Mathematical Reviews number (MathSciNet)**

MR1241042

**Zentralblatt MATH identifier**

0799.68052

**JSTOR**

links.jstor.org

**Subjects**

Primary: 68P05: Data structures

Secondary: 90C40: Markov and semi-Markov decision processes 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

**Keywords**

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

#### Citation

Chassaing, Philippe. Optimality of Move-to-Front for Self-Organizing Data Structures with Locality of References. Ann. Appl. Probab. 3 (1993), no. 4, 1219--1240. doi:10.1214/aoap/1177005280. https://projecteuclid.org/euclid.aoap/1177005280