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
Conflict-Free colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Deterministic conflict-free coloring for intervals: From offline to online
ACM Transactions on Algorithms (TALG)
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
ACM Transactions on Algorithms (TALG)
Dynamic Offline Conflict-Free Coloring for Unit Disks
Approximation and Online Algorithms
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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We provide a framework for online conflict-free coloring (CFcoloring) of any hypergraph. We use this framework to obtain an efficient randomized online algorithm for CF-coloring any k-degenerate hypergraph. Our algorithm uses O(k log n) colors with high probability and this bound is asymptotically optimal for any constant k. Moreover, our algorithm uses O(k log k log n) random bits with high probability. As a corollary, we obtain asymptotically optimal randomized algorithms for online CF-coloring some hypergraphs that arise in geometry. Our algorithm uses exponentially fewer random bits compared to previous results. We introduce deterministic online CF-coloring algorithms for points on the line with respect to intervals and for points on the plane with respect to halfplanes (or unit discs) that use Θ(log n) colors and recolor O(n) points in total.