Randomized algorithms
Coloring graphs with sparse neighborhoods
Journal of Combinatorial Theory Series B
Online conflict-free coloring for intervals
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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 colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic conflict-free coloring for intervals: From offline to online
ACM Transactions on Algorithms (TALG)
Coloring Axis-Parallel Rectangles
Computational Geometry and Graph Theory
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 colourings of graphs and hypergraphs
Combinatorics, Probability and Computing
Notes: Coloring axis-parallel rectangles
Journal of Combinatorial Theory Series A
Online conflict-free colouring for hypergraphs
Combinatorics, Probability and Computing
The potential to improve the choice: list conflict-free coloring for geometric hypergraphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Coloring half-planes and bottomless rectangles
Computational Geometry: Theory and Applications
Proceedings of the twenty-eighth annual symposium on Computational geometry
Online conflict-free colorings for hypergraphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Given a set of points P ⊆ R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with Õ(nβ+ε) colors in expected polynomial time, for any arbitrarily small ε 0 and β = 3?√52 O(√nlog log n/ log n).