Economical Caching with Stochastic Prices
Englert, M., Vocking, B. and Winkler, M. (2009) Economical Caching with Stochastic Prices. In: Stochastic Algorithms: Foundations and Applications. Lecture Notes in Computer Science, 5792 . Springer Verlag, pp. 179-190. ISBN 978-3-642-04943-9
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Official URL: http://dx.doi.org/10.1007/978-3-642-04944-6_15
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 ∈ [α,β], where β > α ≥ 0 and c i ∈ ℕ. 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 c i and put the remaining units into the storage.
In this paper, we study the economical caching problem in a probabilistic analysis, that is, we assume that the prices are generated by a random walk with reflecting boundaries α and β. 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.
|Item Type:||Book Section|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty of Science > Computer Science|
|Depositing User:||Ms Saima Arif|
|Date Deposited:||23 Dec 2010 14:09|
|Last Modified:||26 Jul 2011 12:15|
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