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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 |

Official 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 |

Data sourced from Thomson Reuters' Web of Knowledge

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