An Optimal Offline Algorithm for List Update

TL;DR

This paper characterizes the optimal offline list update strategy through initial permutations and element transfers, and presents an algorithm with factorial time complexity for solving the static list update problem.

Contribution

It introduces a novel characterization of optimal list reorganizations and develops an exact algorithm with specific time complexity for the static list update problem.

Findings

Provides a characterization of optimal list updates using initial permutations and element transfers.

Designs an $O(l^{2} (l-1)!m)$ time algorithm for the static list update problem.

Achieves optimal offline solutions for list reorganization problems.

Abstract

For the static list update problem, given an ordered list $\rho_0$ (an ordering of the list $L$ = \{ $a_a, a_2, ..., a_l$ \}), and a sequence $\sigma = (\sigma_1, \sigma_2, ..., \sigma_m)$ of requests for items in $L$, we characterize the list reorganizations in an optimal offline solution in terms of an initial permutation of the list followed by a sequence of $m$ {\em element transfers}, where an element transfer is a type of list reorganization where only the requested item can be moved. Then we make use of this characterization to design an $O(l^{2} (l-1)!m)$ time optimal offline algorithm.