  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.
