## Computer Science Technical Reports

Technical Report

12-1-1996

PCS-TR96-302

#### Abstract

Koutsoupias and Papadimitriou recently raised the question of how well deterministic on-line paging algorithms can do against a certain class of adversarially biased random inputs. Such an input is given in an on-line fashion; the adversary determines the next request probabilistically, subject to the constraint that no page may be requested with probability more than a fixed $\epsilon>0$. In this paper, we answer their question by estimating, within a factor of two, the optimal competitive ratio of any deterministic on-line strategy against this adversary. We further analyze randomized on-line strategies, obtaining upper and lower bounds within a factor of two. These estimates reveal the qualitative changes as $\epsilon$ ranges continuously from 1 (the standard model) towards 0 (a severely handicapped adversary). The key to our upper bounds is a novel charging scheme that is appropriate for adversarially biased random inputs. The scheme adjusts the costs of each input so that the expected cost of a random input is unchanged, but working with adjusted costs, we can obtain worst-case bounds on a per-input basis. This lets us use worst-case analysis techniques while still thinking of some of the costs as expected costs.

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