Randomized algorithms
Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
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
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)
Dynamic Offline Conflict-Free Coloring for Unit Disks
Approximation and Online Algorithms
Online conflict-free colouring for hypergraphs
Combinatorics, Probability and Computing
Graph unique-maximum and conflict-free colorings
Journal of Discrete Algorithms
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Ordered coloring grids and related graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Graph unique-maximum and conflict-free colorings
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Unique-maximum and conflict-free coloring for hypergraphs and tree graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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 the range space ($P,\mathcal{R}$), where P is a set of n points in ℝ2 and $\mathcal{R}$ is the family of subsets of P induced by all axis-parallel rectangles, the conflict-free coloring problem asks for a coloring of P with the minimum number of colors such that ($P,\mathcal{R}$) is conflict-free. We study the following question: Given P, is it possible to add a small set of points Q such that ($P \cup Q,\mathcal{R}$) can be colored with fewer colors than ($P,\mathcal{R}$)? Our main result is the following: given P, and any ε≥0, one can always add a set Q of O(n1−ε) points such that P ∪ Q can be conflict-free colored using $\tilde{O}(n^{\frac{3}{8}(1+\varepsilon)})$ colors. Moreover, the set Q and the conflict-free coloring can be computed in polynomial time, with high probability. Our result is obtained by introducing a general probabilistic re-coloring technique, which we call quasi-conflict-free coloring, and which may be of independent interest. A further application of this technique is also given.