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)
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
Static and dynamic algorithms for k-point clustering problems
Journal of Algorithms
A practical map labeling algorithm
Computational Geometry: Theory and Applications
A polynomial time solution for labeling a rectilinear map
Information Processing Letters
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
New Algorithms for Two-Label Point Labeling
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
A Factor-2 Approximation for Labeling Points with Maximum Sliding Labels
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
New Algorithms for Two-Label Point Labeling
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Incremental labeling in closed-2PM model
Computers and Electrical Engineering
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 label shape L and a set of n points in the plane, the 2-label point-labeling problem consists of placing 2n nonintersecting translated copies of L of maximum size such that each point touches two unique copies--its labels. In this paper we give new and simple approximation algorithms for L an axis-parallel square or a circle. For squares we improve the best previously known approximation factor from 1/3 to 1/2 . For circles the improvement from 1/2 to ≈ 0.513 is less significant, but the fact that 1/2 is not best possible is interesting in its own right. For the decision version of the latter problem we have an NP-hardness proof that also shows that it is NP-hard to approximate the label size beyond a factor of ≈ 0.732. As their predecessors, our algorithms take O(n log n) time and O(n) space.