Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
On the chromatic number of some geometric hypergraphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Conflict-free colorings of shallow discs
Proceedings of the twenty-second annual symposium on Computational geometry
How to play a coloring game against a color-blind adversary
Proceedings of the twenty-second annual symposium on Computational geometry
Conflict-free coloring for intervals: from offline to online
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Conflict-free coloring for rectangle ranges using O(n.382) colors
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Online Conflict-Free Coloring for Intervals
SIAM Journal on Computing
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
ACM Transactions on Algorithms (TALG)
Conflict-Free colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Online conflict-free colorings for hypergraphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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A conflict-free coloring for a given set of disks is a coloring of the disks such that for any point p on the plane there is a disk among the disks covering p having a color different from that of the rest of the disks that covers p. In the dynamic offline setting, a sequence of disks is given, we have to color the disks one-by-one according to the order of the sequence and maintain the conflict-free property at any time for the disks that are colored. This paper focuses on unit disks, i.e., disks with radius one. We give an algorithm that colors a sequence of n unit disks in the dynamic offline setting using O(logn) colors. The algorithm is asymptotically optimal because Ω(logn) colors is necessary to color some set of n unit disks for any value of n [9].