## Abstract

The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server si lies in its own metric space Mi. A request is a ktuple r = (r1; r2; : : : ; rk) and to serve it, we need to move some server si to the point ri ϵ Mi, and the goal is to minimize the total distance traveled by the servers. Despite much work, no f(k)-competitive algorithm is known for the problem for k > ϵ servers, even for special cases such as uniform metrics and lines. Here, we consider the problem in uniform metrics and give the first f(k)-competitive algorithms for general k. In particular, we obtain deterministic and randomized algorithms with competitive ratio k > 2k and O(k3 log k) respectively. Our deterministic bound is based on a novel application of the polynomial method to online algorithms, and essentially matches the long-known lower bound of 2k -1. We also give a 22O(k) -competitive deterministic algorithm for weighted uniform metrics, which also essentially matches the recent doubly exponential lower bound for the problem.

Original language | English |
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Title of host publication | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |

Editors | Artur Czumaj |

Publisher | Society for Industrial and Applied Mathematics (SIAM) |

Pages | 992-1001 |

Number of pages | 10 |

ISBN (Electronic) | 9781611975031 |

DOIs | |

Publication status | Published - 2018 |

Event | 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018) - Astor Crowne Plaza, New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018 Conference number: 29 https://www.siam.org/meetings/da18/ |

### Conference

Conference | 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018) |
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Abbreviated title | SODA 2018 |

Country/Territory | United States |

City | New Orleans |

Period | 7/01/18 → 10/01/18 |

Internet address |