### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 98-108 |

Number of pages | 11 |

Volume | 2161 |

ISBN (Print) | 9783540424932 |

Publication status | Published - 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2161, pp. 98-108). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2161). Springer Verlag.

**Buying a constant competitive ratio for paging.** / Csirik, J.; Imreh, Csanád; Noga, John; Seiden, Steve S.; Woeginger, Gerhard J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2161, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2161, Springer Verlag, pp. 98-108, 9th Annual European Symposium on Algorithms, ESA 2001, Arhus, Denmark, 8/28/01.

}

TY - GEN

T1 - Buying a constant competitive ratio for paging

AU - Csirik, J.

AU - Imreh, Csanád

AU - Noga, John

AU - Seiden, Steve S.

AU - Woeginger, Gerhard J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84943233742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943233742&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540424932

VL - 2161

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 98

EP - 108

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -