### Abstract

We show that for any set of n moving points in R^{d} and any parameter 2 ≤ k ≤ n, one can select a fixed non-empty subset of the points of size O(k log k), such that the Voronoi diagram of this subset is "balanced" at any given time (i.e., it contains O(n/k) points per cell). We also show that the bound O(k log k) is near optimal even for the one dimensional case in which points move linearly in time. As an application, we show that one can assign communication radii to the sensors of a network of n moving sensors so that at any given time, their interference is O(√n log n). This is optimal up to an O(√log n) factor.

Original language | English |
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Title of host publication | 24th Annual European Symposium on Algorithms, ESA 2016 |

Editors | Christos Zaroliagis, Piotr Sankowski |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770156 |

DOIs | |

Publication status | Published - 2016 Aug 1 |

Event | 24th Annual European Symposium on Algorithms, ESA 2016 - Aarhus, Denmark Duration: 2016 Aug 22 → 2016 Aug 24 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 57 |

ISSN (Print) | 1868-8969 |

### Other

Other | 24th Annual European Symposium on Algorithms, ESA 2016 |
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Country | Denmark |

City | Aarhus |

Period | 16/8/22 → 16/8/24 |

### Keywords

- Facility location
- Interference minimization
- Moving points
- Range spaces
- Voronoi diagrams

### ASJC Scopus subject areas

- Software

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## Cite this

*24th Annual European Symposium on Algorithms, ESA 2016*[34] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 57). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2016.34