## Abstract

We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer c_{i} to facility f_{j} before the next customer c_{i+1} arrives. The cost of this assignment is the distance between c_{i} and f_{j}. The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. We also consider a slightly more general situation where different facilities may have different capacities. Finally, we study a variant of the online facility assignment problem in which the facilities are placed on the vertices of a graph and present two algorithms for that setting.

Original language | English (US) |
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Pages (from-to) | 455-467 |

Number of pages | 13 |

Journal | Theoretical Computer Science |

Volume | 806 |

DOIs | |

State | Published - Feb 2 2020 |

Externally published | Yes |

## Keywords

- Greedy algorithms
- Online facility assignment

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science