Abstract |
In the economical caching problem, an online algorithm is given a sequence of prices for a certain commodity. The algorithm has to manage a buffer of fixed capacity over time. We assume that time proceeds in discrete steps. In step i, the commodity is available at price c_i \in [\alpha; \bet], where \beta > \alpha \geq 0. One unit of the commodity is consumed per step. The algorithm can buy this unit at the current price c_i, can take a previously bought unit from the storage, or can buy more than one unit at price ci and put the remaining units into the storage. We study the economical caching problem in a probabilistic analysis, that is, we assume that the prices are generated by a random walk with refl ecting boundaries \alpha and \beta. We are able to identify the optimal online algorithm in this probabilistic model and analyze its expected cost and its expected savings, i.e., the cost that it saves in comparison to the cost that would arise without having a buffer. In particular, we compare the savings of the optimal online algorithm with the savings of the optimal offline algorithm in a probabilistic competitive analysis and obtain tight bounds (up to constant factors) on the ratio between the expected savings of these two algorithms. |