Abstract
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 non-conflicting 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.
This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under grants Wa 1066/1-1, 3-1, and 3-2
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Keywords
- Simulated Annealing
- Greedy Algorithm
- Constraint Satisfaction Problem
- Polynomial Time Approximation Scheme
- Local Consistency
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© 1998 Springer-Verlag Berlin Heidelberg
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Wagner, F., Wolff, A. (1998). A Combinatorial Framework for Map Labeling. In: Whitesides, S.H. (eds) Graph Drawing. GD 1998. Lecture Notes in Computer Science, vol 1547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37623-2_24
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DOI: https://doi.org/10.1007/3-540-37623-2_24
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