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Discrete & Computational Geometry
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Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
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SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Coloring graphs with sparse neighborhoods
Journal of Combinatorial Theory Series B
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
The discrepancy method: randomness and complexity
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FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Online conflict-free coloring for intervals
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
ACM SIGACT News
The Minimum Independence Number of a Hasse Diagram
Combinatorics, Probability and Computing
Conflict-free coloring of unit disks
Discrete Applied Mathematics
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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In this paper, we study coloring problems related to frequency assignment problems in cellular networks. In abstract setting, the problems are of the following two types:CF-coloring of regions: Given a finite family S of n regions of some fixed type (such as discs, pseudo-discs, axis-parallel rectangles, etc.), what is the minimum integer k, such that one can assign a color to each region of S, using a total of at most k colors, such that the resulting coloring has the following property: For each point p ∈b∈S b there is at least one region b∈S that contains p in its interior, whose color is unique among all regions in S that contain p in their interior (in this case we say that p is being `served' by that color). We refer to such a coloring as a conflict-free coloring of S (CF-coloring in short).CF-coloring of a range space: Given a set P of n points in Rd and a set R of ranges (for example, the set of all discs in the plane), what is the minimum integer k, such that one can color the points of P by k colors, so that for any r ∈ R with P∩r∈≠Ø, there is at least one point q ∈ P ∩ r that is assigned a unique color among all colors assigned to points of P ∩ r (in this case we say that r is 'served' by that color). We refer to such a coloring as a conflict-free coloring of (P,R) (CF-coloring in short).