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An Algorithmic Framework for Labeling Network Maps

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Abstract

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of metro maps. We present a flexible and versatile labeling model that subsumes different labeling styles. We show that labeling a single line of the network is NP-hard, even if we make very restricting requirements about the labeling style that is used with this model. For a restricted variant of that model, we then introduce an efficient algorithm that optimally labels a single line with respect to a given cost function. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.

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Acknowledgements

We sincerely thank Herman Haverkort, Arlind Nocaj, Aidan Slingsby and Jo Wood for helpful and interesting discussions.

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Correspondence to Benjamin Niedermann.

Additional information

A preliminary version of this paper has appeared in Proc. 21st Int. Conf. on Computing Combinatorics (COCOON’15), volume 9198 of Lect. Notes Comput. Sci., pages 689–700, Springer-Verlag. This research was initiated during Dagstuhl Seminar 13151 “Drawing Graphs and Maps with Curves” in April 2013.

Appendix: Labelings

Appendix: Labelings

See Figs. 15, 16, 17, 18, 19, 20 and 21.

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Labelings for instance Sydney1. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

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Labelings for instance Sydney2. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

Fig. 17
figure 17

Labelings for instance Sydney3. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

Fig. 18
figure 18

Labelings for instance Sydney4. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

Fig. 19
figure 19

Labelings for instance Vienna1. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

Fig. 20
figure 20

Labelings for instance Vienna2. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

Fig. 21
figure 21

Labelings for instance Vienna3. a DpAlg, b GreedyAlg, c ScaleAlg, d IlpAlg

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Niedermann, B., Haunert, JH. An Algorithmic Framework for Labeling Network Maps. Algorithmica 80, 1493–1533 (2018). https://doi.org/10.1007/s00453-017-0350-0

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  • DOI: https://doi.org/10.1007/s00453-017-0350-0

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