### Samenvatting

We introduce the fully-dynamic conflict-free coloring problem for a set S of intervals in 1 with respect to points, where the goal is to maintain a conflict-free coloring for S under insertions and deletions. A coloring is conflict-free if for each point p contained in some interval, p is contained in an interval whose color is not shared with any other interval containing p. We investigate trade-offs between the number of colors used and the number of intervals that are recolored upon insertion or deletion of an interval. Our results include: a lower bound on the number of recolorings as a function of the number of colors, which implies that with O(1) recolorings per update the worst-case number of colors is ω(log n/loglog n), and that any strategy using O(1/) colors needs ω(n) recolorings; a coloring strategy that uses O(log n) colors at the cost of O(log n) recolorings, and another strategy that uses O(1/) colors at the cost of O(n/) recolorings; stronger upper and lower bounds for special cases. We also consider the kinetic setting where the intervals move continuously (but there are no insertions or deletions); here we show how to maintain a coloring with only four colors at the cost of three recolorings per event and show this is tight.

Originele taal-2 | Engels |
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Pagina's (van-tot) | 49-72 |

Aantal pagina's | 24 |

Tijdschrift | International Journal of Computational Geometry and Applications |

Volume | 29 |

Nummer van het tijdschrift | 1 |

DOI's | |

Status | Gepubliceerd - 1 mrt 2019 |

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## Citeer dit

*International Journal of Computational Geometry and Applications*,

*29*(1), 49-72. https://doi.org/10.1142/S021819591940003X