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- W4300944981 abstract "We introduce the fully-dynamic conflict-free coloring problem for a set $S$ of intervals in $mathbb{R}^1$ 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 $Omega(log n/loglog n)$, and that any strategy using $O(1/varepsilon)$ colors needs $Omega(varepsilon n^{varepsilon})$ recolorings; - a coloring strategy that uses $O(log n)$ colors at the cost of $O(log n)$ recolorings, and another strategy that uses $O(1/varepsilon)$ colors at the cost of $O(n^{varepsilon}/varepsilon)$ 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." @default.
- W4300944981 created "2022-10-04" @default.
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- W4300944981 date "2017-01-12" @default.
- W4300944981 modified "2023-09-27" @default.
- W4300944981 title "Fully-Dynamic and Kinetic Conflict-Free Coloring of Intervals with Respect to Points" @default.
- W4300944981 doi "https://doi.org/10.48550/arxiv.1701.03388" @default.
- W4300944981 hasPublicationYear "2017" @default.
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