On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Restricted colorings of graphs
Surveys in combinatorics, 1993
Every planar graph is 5-choosable
Journal of Combinatorial Theory Series B
Discrete Mathematics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Choosability in random hypergraphs
Journal of Combinatorial Theory Series B
On Vertex Ranking for Permutations and Other Graphs
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
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
On The Chromatic Number of Geometric Hypergraphs
SIAM Journal on Discrete Mathematics
Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles
Random Structures & Algorithms - Proceedings of the Thirteenth International Conference “Random Structures and Algorithms” held May 28–June 1, 2007, Tel Aviv, Israel
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
ACM Transactions on Algorithms (TALG)
Conflict-free coloring of unit disks
Discrete Applied Mathematics
Conflict-free coloring
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
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Graph unique-maximum and conflict-free colorings
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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Given a geometric hypergraph (or a range-space) H=(V,E), a coloring of its vertices is said to be conflict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The study of this notion is motivated by frequency assignment problems in wireless networks. We study the list-coloring (or choice) version of this notion. In this version, each vertex is associated with a set of (admissible) colors and it is allowed to be colored only with colors from its set. List coloring arises naturally in the context of wireless networks. Our main result is a list coloring algorithm based on a new potential method. The algorithm produces a stronger unique-maximum coloring, in which colors are positive integers and the maximum color in every hyperedge occurs uniquely. As a corollary, we provide asymptotically sharp bounds on the size of the lists required to assure the existence of such unique-maximum colorings for many geometric hypergraphs (e.g., discs or pseudo-discs in the plane or points with respect to discs). Moreover, we provide an algorithm, such that, given a family of lists with the appropriate sizes, computes such a coloring from these lists.