On the List Update Problem with Advice

TL;DR

This paper investigates the advice complexity of the online list update problem, showing that minimal advice can significantly improve competitive ratios and that certain algorithms can be optimized with just a few advice bits.

Contribution

It demonstrates that linear advice is needed for optimality, while just two bits suffice to surpass the 2-competitive lower bound, and it analyzes the competitiveness of MTF2 algorithms.

Findings

Linear advice suffices for optimal or near-optimal solutions.

Two advice bits can reduce the competitive ratio below 2.

MTF2 algorithms are proven to be 2.5-competitive.

Abstract

We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than $15/14$. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of $2$ on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of $5/3$. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, TIMESTAMP and two members of the MTF2 family of algorithms. We also show that MTF2 algorithms are $2.5$-competitive.