A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
A practical map labeling algorithm
Computational Geometry: Theory and Applications
Map labeling and its generalizations
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Point labeling with sliding labels
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Point set labeling with specified positions
Proceedings of the sixteenth annual symposium on Computational geometry
Efficient Approximation Algorithms for Multi-label Map Labeling
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Polynomial Time Algorithms for Three-Label Point Labeling
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
New bounds on map labeling with circular labels
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Given a set P of n points in the plane, the two-circle point-labeling problem consists of placing 2n uniform, non-intersecting, maximum-size open circles such that each point touches exactly two circles. It is known that it is NP-hard to approximate the label size beyond a factor of ≈ 0:7321. In this paper we improve the best previously known approximation factor from ≈ 0:51 to 2/3. We keep the O(n log n) time and O(n) space bounds of the previous algorithm. As in the previous algorithm we label each point within its Voronoi cell. Unlike that algorithm we explicitely compute the Voronoi diagram, label each point optimally within its cell, compute the smallest label diameter over all points and finally shrink all labels to this size.