## Abstract

We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain R of normalized dimensions of 1 and ρ≥ 1 , and distances are measured according to the Manhattan metric. We show that the family of balanced facility configurations (in which the Voronoi cells of individual facilities are equalized with respect to a number of geometric properties) is considerably richer in this metric than for Euclidean distances. Our main result considers the One-Round Voronoi Game with Manhattan distances, in which first player White and then player Black each place n points in R; each player scores the area for which one of its facilities is closer than the facilities of the opponent. We give a tight characterization: White has a winning strategy if and only if ρ≥ n; for all other cases, we present a winning strategy for Black.

Original language | English |
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Pages (from-to) | 79-101 |

Number of pages | 23 |

Journal | Annals of Operations Research |

Volume | 321 |

Issue number | 1-2 |

Early online date | 5 Dec 2022 |

DOIs | |

Publication status | E-pub ahead of print - 5 Dec 2022 |

## Keywords

- competitive location
- facility location
- geometric optimization
- Manhattan distances
- Voronoi game