The Complexity of Paging Against a Probabilistic Adversary.

We consider deterministic online algorithms for paging. The offline version of the paging problem, in which the whole input is given in advance, is known to be easily solvable. If the input is random, chosen according to some known probability distribution, an $$\mathcal {O}\mathopen {}\left \log k\right $$-competitive algorithm exists. Moreover, there are distributions, where no algorithm can be better than $$\mathrm {\Omega }\mathopen {}\left \log k\right $$-competitive. In this paper, we ask the question of what happens if it is known that the input is one from a set of $$\ell $$ potential candidates, chosen according to some probability distribution. We present an $$\mathcal {O}\mathopen {}\left \log \ell \right $$-competitive algorithm, and show a matching lower bound.