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. Despite its simplicity, we prove that it is NP-complete to label a single line of the network. For a restricted variant of that model, we introduce an efficient algorithm that optimally labels a single line. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.
This work was started at the seminar “Drawing Graphs and Maps with Curves” organized by S. Fabrikant, S. G. Kobourov, M. Nöllenburg and M. Teillaud; Schloss Dagstuhl, Germany, April 2013
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Comp. Geom.-Theor. Appl. 11, 209–218 (1998)
Christensen, J., Marks, J., Shieber, S.: An empirical study of algorithms for point-feature label placement. Acm. T. Graphic. 14(3), 203–232 (1995)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)
Fink, M., Haverkort, H., Nöllenburg, M., Roberts, M., Schuhmann, J., Wolff, A.: Drawing metro maps using Bézier curves. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 463–474. Springer, Heidelberg (2013)
Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: ACM Sympos. on Comput. Geom., pp. 281–288 (1991)
Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are np-complete. Inf. Process. Lett. 12(3), 133–137 (1981)
Haunert, J.-H., Niedermann, B.: An algorithmic framework for labeling network maps (2015). CoRR, abs/1505.00164
Imhof, E.: Positioning names on maps. Am. Cartographer, 128–144 (1975)
Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329–343 (1982)
Nöllenburg, M., Wolff, A.: Drawing and labeling high-quality metro maps by mixed-integer programming. IEEE T. Vis. Comput. Gr. 17(5), 626–641 (2011)
Stott, J., Rodgers, P., Martinez-Ovando, J., Walker, S.: Automatic metro map layout using multicriteria optimization. IEEE T. Vis. Comput. Gr. 17(1), 101–114 (2011)
van Goethem, A., Meulemans, W., Reimer, A., Haverkort, H., Speckmann, B.: Topologically safe curved schematisation. Cartogr. J. 50(3), 276–285 (2013)
Wang, Y.-S., Chi, M.-T.: Focus+context metro maps. IEEE T. Vis. Comput. Gr. 17(12), 2528–2535 (2011)
Wolff, A.: Graph drawing and cartography. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization, chapter 23, pp. 697–736. CRC Press (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Haunert, JH., Niedermann, B. (2015). An Algorithmic Framework for Labeling Network Maps. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_54
Download citation
DOI: https://doi.org/10.1007/978-3-319-21398-9_54
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21397-2
Online ISBN: 978-3-319-21398-9
eBook Packages: Computer ScienceComputer Science (R0)