Optimal Bounds for Online Page Migration with Generalized Migration Costs

This paper attends to a generalized version of the classic page migration problem where migration costs are not necessarily given by the migration distance only, but may depend on prior migrations, or on the available bandwidth along the migration path. Interestingly, this problem cannot be viewed from a Metrical Task System (MTS) perspective, despite the generality of MTS: The corresponding MTS has an unbounded state space and, thus, an unbounded competitive ratio. Nevertheless, we are able to present an optimal online algorithm for a wide range of problem variants, improving the best upper bounds known so far for more specific problems. For example, we present a tight bound of Θ(log n / log log n) for the competitive ratio of the virtual server migration problem introduced recently. I