### Abstract

We consider a variant of the online paging problem where the online algorithm may buy additional cache slots at a certain cost. The overall cost incurred equals the total cost for the cache plus the number of page faults. This problem and our results are a generalization of both, the classical paging problem and the ski rental problem. We derive the following three tight results: (1) For the case where the cache cost depends linearly on the cache size, we give a λ-competitive online algorithm where λ ≈ 3:14619 is a solution of λ = 2 + ln λ. This competitive ratio λ is best possible. (2) For the case where the cache cost grows like a polynomial of degree d in the cache size, we give an online algorithm whose competitive ratio behaves like d/ ln d + o(d/ ln d). No online algorithm can reach a competitive ratio better than d/ ln d. (3) We exactly characterize the class of cache cost functions for which there exist online algorithms with finite competitive ratios.

Original language | English |
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Title of host publication | Algorithms - ESA 2001 - 9th Annual European Symposium, Proceedings |

Editors | Friedhelm Meyer auf der Heide |

Publisher | Springer Verlag |

Pages | 98-108 |

Number of pages | 11 |

ISBN (Print) | 9783540424932 |

Publication status | Published - Jan 1 2001 |

Event | 9th Annual European Symposium on Algorithms, ESA 2001 - Arhus, Denmark Duration: Aug 28 2001 → Aug 31 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2161 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 9th Annual European Symposium on Algorithms, ESA 2001 |
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Country | Denmark |

City | Arhus |

Period | 8/28/01 → 8/31/01 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms - ESA 2001 - 9th Annual European Symposium, Proceedings*(pp. 98-108). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2161). Springer Verlag.