### Abstract

Original language | English |
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Title of host publication | 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 15-17 October 2017, Berkeley, California |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 493-504 |

ISBN (Electronic) | 978-1-5386-3464-6 |

ISBN (Print) | 978-1-5386-3465-3 |

DOIs | |

Publication status | Published - 2017 |

Event | 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017), October 15-17, 2017, Berkeley, California - DoubleTree Hotel at the Berkeley Marina, Berkeley, United States Duration: 15 Oct 2017 → 17 Oct 2017 https://focs17.simons.berkeley.edu/ |

### Conference

Conference | 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017), October 15-17, 2017, Berkeley, California |
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Abbreviated title | FOCS 2017 |

Country | United States |

City | Berkeley |

Period | 15/10/17 → 17/10/17 |

Internet address |

### Fingerprint

### Cite this

*2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 15-17 October 2017, Berkeley, California*(pp. 493-504). Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/FOCS.2017.52

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*2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 15-17 October 2017, Berkeley, California.*Institute of Electrical and Electronics Engineers, Piscataway, pp. 493-504, 58th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2017), October 15-17, 2017, Berkeley, California, Berkeley, United States, 15/10/17. https://doi.org/10.1109/FOCS.2017.52

**Weighted k-server bounds via combinatorial dichotomies.** / Bansal, N.; Elias, M.; Koumoutsos, G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Weighted k-server bounds via combinatorial dichotomies.

AU - Bansal, N.

AU - Elias, M.

AU - Koumoutsos, G.

PY - 2017

Y1 - 2017

N2 - The weighted k-server problem is a natural generalization of the k-server problem where each server has a different weight. We consider the problem on uniform metrics, which corresponds to a natural generalization of paging. Our main result is a doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap. The lower bound is based on relating the weighted k-server problem to a certain combinatorial problem and proving a Ramsey-theoretic lower bound for it. This combinatorial connection also reveals several structural properties of low cost feasible solutions to serve a sequence of requests. We use this to show that the generalized Work Function Algorithm achieves an almost optimum competitive ratio, and to obtain new refined upper bounds on the competitive ratio for the case of d different weight classes.

AB - The weighted k-server problem is a natural generalization of the k-server problem where each server has a different weight. We consider the problem on uniform metrics, which corresponds to a natural generalization of paging. Our main result is a doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap. The lower bound is based on relating the weighted k-server problem to a certain combinatorial problem and proving a Ramsey-theoretic lower bound for it. This combinatorial connection also reveals several structural properties of low cost feasible solutions to serve a sequence of requests. We use this to show that the generalized Work Function Algorithm achieves an almost optimum competitive ratio, and to obtain new refined upper bounds on the competitive ratio for the case of d different weight classes.

U2 - 10.1109/FOCS.2017.52

DO - 10.1109/FOCS.2017.52

M3 - Conference contribution

SN - 978-1-5386-3465-3

SP - 493

EP - 504

BT - 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 15-17 October 2017, Berkeley, California

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -