A Combinatorial Framework for Map Labeling

  • Frank Wagner
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


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.


Simulated Annealing Greedy Algorithm Constraint Satisfaction Problem Polynomial Time Approximation Scheme Local Consistency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Frank Wagner
    • 1
  • Alexander Wolff
    • 1
  1. 1.Institut fr InformatikFachbereich Mathematik und InformatikGermany

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