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Economical caching with stochastic prices

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Englert, Matthias, Voecking, Berthold and Winkler, Melanie (2009) Economical caching with stochastic prices. In: Watanabe, O and Zeugmann, T, (eds.) Stochastic Algorithms : Foundations and Applications. Lecture Notes in Computer Science, Volume 5792 . Springer, pp. 179-190. ISBN 9783642049439

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Official URL: http://dx.doi.org/10.1007/978-3-642-04944-6_15

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) is an element of [alpha, beta], where beta > alpha >= 0 and c(i) is an element of 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 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.

Item Type:	Book Item
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Series Name:	Lecture Notes in Computer Science
Journal or Publication Title:	Stochastic Algorithms : Foundations and Applications
Publisher:	Springer
ISBN:	9783642049439
ISSN:	0302-9743
Book Title:	Stochastic Algorithms : Foundations and Applications
Editor:	Watanabe, O and Zeugmann, T
Date:	2009
Volume:	Volume 5792
Number of Pages:	12
Page Range:	pp. 179-190
Identification Number:	10.1007/978-3-642-04944-6_15
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	DFG, Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GK/1298 “AlgoSyn” (DFG); EP/F043333/1 (EPSRC)
Conference Paper Type:	Paper
Title of Event:	5th International Symposium on Stochastic Algorithms - Foundations and Applications
Type of Event:	Conference
Location of Event:	Hokkaido Univ, Sapporo, JAPAN
Date(s) of Event:	OCT 26-28, 2009
URI:	http://wrap.warwick.ac.uk/id/eprint/6526