Englert, Matthias, Röglin, Heiko, Spönemann, Jacob and Vöcking, Berthold (2009) Economical caching. In: 26th International Symposium on Theoretical Aspects of Computer Science, Freiburg, Germany, Feb 2009. Published in: Leibniz International Proceedings in Informatics (LIPIcs), Volume 3 pp. 385-396.
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Official URL: http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1826
We study the management of buffers and storages in environments with unpredictably varying prices in a competitive analysis. In the economical caching problem, there is a storage with a certain capacity. For each time step, an online algorithm is given a price from the interval [1, α], a consumption, and possibly a buying limit. The online algorithm has to decide the amount to purchase from some commodity, knowing the parameter α but without knowing how the price evolves in the future. The algorithm can purchase at most the buying limit. If it purchases more than the current consumption, then the excess is stored in the storage; otherwise, the gap between consumption and purchase must be taken from the storage. The goal is to minimize the total cost. Interesting applications are, for example, stream caching on mobile devices with different classes of service, battery management in micro hybrid cars, and the efficient purchase of resources. First we consider the simple but natural class of algorithms that can informally be described as memoryless. We show that these algorithms cannot achieve a competitive ratio below √α. Then we present a more sophisticated deterministic algorithm achieving a competitive ratio of 1/W(1−α/eα)+1 E [√α/√2, √α+1/√2], where W denotes the Lambert W function. We prove that this algorithm is optimal and that not even randomized online algorithms can achieve a better competitive ratio. On the other hand, we show how to achieve a constant competitive ratio if the storage capacity of the online algorithm exceeds the storage capacity of an optimal offline algorithm by a factor of log α.
|Item Type:||Conference Item (Paper)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software|
|Divisions:||Faculty of Science > Computer Science|
|Library of Congress Subject Headings (LCSH):||Cache memory -- Mathematical models, Buffer storage (Computer science) -- Mathematical models|
|Journal or Publication Title:||Leibniz International Proceedings in Informatics (LIPIcs)|
|Publisher:||Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik|
|Official Date:||February 2009|
|Page Range:||pp. 385-396|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), Deutsche Forschungsgemeinschaft (DFG), Deutscher Akademischer Austauschdienst (DAAD)|
|Grant number:||EP/F043333/1 (EPSRC), WE 2842/1 (DFG), 1298 (DFG)|
|Conference Paper Type:||Paper|
|Title of Event:||26th International Symposium on Theoretical Aspects of Computer Science|
|Type of Event:||Conference|
|Location of Event:||Freiburg, Germany|
|Date(s) of Event:||Feb 2009|
 Allan Borodin and Ran El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998.
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