Motivated by fairness requirements in communication networks, we introduce a natural variant of the online paging problem, called \textit{min-max} paging, where the objective is to minimize the maximum number of faults on any page. While the classical paging problem, whose objective is to minimize the total number of faults, admits $k$-competitive deterministic and $O(\log k)$-competitive randomized algorithms, we show that min-max paging does not admit a $c(k)$-competitive algorithm for any function $c$. Specifically, we prove that the randomized competitive ratio of min-max paging is $\Omega(\log(n))$ and its deterministic competitive ratio is $\Omega(k\log(n)/\log(k))$, where $n$ is the total number of pages ever requested. We design a fractional algorithm for paging with a more general objective -- minimize the value of an $n$-variate differentiable convex function applied to the vector of the number of faults on each page. This gives an $O(\log(n)\log(k))$-competitive fractional algorithm for min-max paging. We show how to round such a fractional algorithm with at most a $k$ factor loss in the competitive ratio, resulting in a deterministic $O(k\log(n)\log(k))$-competitive algorithm for min-max paging. This matches our lower bound modulo a $\mathrm{poly}(\log(k))$ factor. We also give a randomized rounding algorithm that results in a $O(\log^2 n \log k)$-competitive algorithm.

翻译：在通信网络的公平性要求驱动下, 我们引入了一个名为\ textit{ min- max} 调制的在线调控问题的自然变体, 其目标在于将任何页面的断层最大数量最小化。 虽然古典调控问题, 其目标在于将断层总数最小化, 承认美元- 有竞争力的确定性 和 $O( log k) 随机化算法。 我们显示 微量成像不接受任何函数的 $( k) 的竞争性算法 。 具体地说, 我们证明, 微量- 市价比的随机竞争性比 $( k) 。 我们证明, 微量- 市价比的随机竞争比 $( 美元) 。 在每页中, 最有竞争力的 美元( 美元) 市价( ) 市- 市价( 市- 市值) 市内, 也显示一个有竞争力的市价因素 。