Online computation and competitive analysis
Online computation and competitive analysis
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
Conflict-Free colorings of rectangles ranges
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Conflict-free colorings of shallow discs
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
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 colourings of graphs and hypergraphs
Combinatorics, Probability and Computing
Online conflict-free colouring for hypergraphs
Combinatorics, Probability and Computing
Online conflict-free colorings for hypergraphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We study the problem of conflict-free (CF) coloring of a set of points in the plane, in an online fashion, with respect to halfplanes, nearly-equal axis-parallel rectangles, and congruent disks. As a warm-up exercise, the online CF coloring of points on the line with respect to intervals is also considered. We present randomized algorithms in the oblivious adversary model, where the adversary does not see the colors used. For the problems considered, the algorithms always produce valid CF colorings, and use O(logn) colors with high probability (these bounds are optimal in the worst case). Our randomized online algorithms are considerably simpler than previous algorithms for this problem and use fewer colors.We also present a deterministic algorithm for the CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using O(polylog(n)) colors. This is the first efficient deterministic online CF coloring algorithm for this problem.