A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Approximate map labeling is in &OHgr;(n log n)
Information Processing Letters
An empirical study of algorithms for point-feature label placement
ACM Transactions on Graphics (TOG)
Empirical testing of algorithms for variable-sized label placement
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Point set labeling with sliding labels
Proceedings of the fourteenth annual symposium on Computational geometry
A unified approach to labeling graphical features
Proceedings of the fourteenth annual symposium on Computational geometry
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
Over-Constrained Systems
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Labeling Points with Rectangles of Various Shapes
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
A topology-shape-metrics approach for the automatic layout of UML class diagrams
Proceedings of the 2003 ACM symposium on Software visualization
Labeling points with given rectangles
Information Processing Letters
Automatic layout of UML class diagrams in orthogonal style
Information Visualization - Special issue: Software visualization
Visual inspection of multivariate graphs
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
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The general map labeling problem consists in labeling a set of sites (points, lines, regions) given a set of candidates (rectangles, circles, ellipses, irregularly shaped labels) for each site. A map can be a classical cartographical map, a diagram, a graph or any other figure that needs to be labeled. A labeling is either a complete set of nonconflicting candidates, one per site, or a subset of maximum cardinality. Finding such a labeling is NP-hard.We present a combinatorial framework to attack the problem in its full generality. The key idea is to separate the geometric from the combinatorial part of the problem. The latter is captured by the conflict graph of the candidates and by rules which successively simplify this graph towards a near-optimal solution.We exemplify this framework at the problem of labeling point sets with axis-parallel rectangles as candidates, four per point. We do this such that it becomes clear how our concept can be applied to other cases. We study competing algorithms and do a thorough empirical comparison. The new algorithm we suggest is fast, simple and effective.