  The list update problem is a classical online problem, with an optimal
competitive ratio that is still open, known to be somewhere between 1.5 and
1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is
COMB, a randomized combination of BIT and the TIMESTAMP algorithm TS. This and
almost all other list update algorithms, like MTF, are projective in the sense
that they can be defined by looking only at any pair of list items at a time.
Projectivity (also known as "list factoring") simplifies both the description
of the algorithm and its analysis, and so far seems to be the only way to
define a good online algorithm for lists of arbitrary length. In this paper we
characterize all projective list update algorithms and show that their
competitive ratio is never smaller than 1.6 in the partial cost model.
Therefore, COMB is a best possible projective algorithm in this model.
