## Abstract

The k-server problem is one of the most fundamental online problems. The problem is to schedule k mobile servers to visit a sequence of points in a metric space with minimum total mileage. The k-server conjecture of Manasse, McGeogh, and Sleator states that there exists a k-competitive online algorithm. The conjecture has been open for over 15 years. The top candidate online algorithm for settling this conjecture is the work function algorithm (WFA) which was shown to have competitive ratio at most 2k-1. In this paper, we lend support to the conjecture that WFA is in fact k-competitive by proving that it achieves this ratio in several special metric spaces: the line, the star, and all metric spaces with k+2 points.

Original language | American English |
---|---|

Pages (from-to) | 337-345 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 324 |

Issue number | 2-3 SPEC. ISS. |

DOIs | |

State | Published - 20 Sep 2004 |

### Bibliographical note

Funding Information:∗Corresponding author. E-mail addresses: yair@cs.huji.ac.il (Y. Bartal), elias@di.uoa.gr (E. Koutsoupias). 1Supported in part by a grant of the Israeli Science Foundation (195/02). 2Supported in part by NSF Grant CCR-0105752.

## Keywords

- Online algorithms
- The k -server problem
- Work function