Label Number Maximization in the Slider Model (Extended Abstract)

Ebner, Dietmar and Klau, Gunnar W. and Weiskircher, René (2004) Label Number Maximization in the Slider Model (Extended Abstract). In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 144-154 (Official URL:

Full text not available from this repository.


We consider the NP-hard label number maximization problem lnm: Given a set of rectangular labels, each of which belongs to a point feature in the plane, the task is to find a labeling for a largest subset of the labels. A labeling is a placement such that none of the labels overlap and each is placed so that its boundary touches the corresponding point feature. The purpose of this paper is twofold: We present a new force-based simulated annealing algorithm to heuristically solve the problem and we provide the results of a very thorough experimental comparison of the best known labeling methods on widely used benchmark sets. The design of our new method has been guided by the goal to produce labelings that are similar to the results of an experienced human performing the same task. So we are not only looking for a labeling where the number of labels placed is high but also where the distribution of the placed labels is good. Our experimental results show that the new algorithm outperforms the other methods in terms of quality while still being reasonably fast and confirm that the simulated annealing method is well-suited for map labeling problems.

Item Type:Conference Paper
Additional Information:10.1007/978-3-540-31843-9_16
Classifications:M Methods > M.400 Force-directed / Energy-based
G Algorithms and Complexity > G.630 Labeling
ID Code:581

Repository Staff Only: item control page


J. Christensen, J. Marks, and S. Shieber. An empirical study of algorithms for point-feature label placement. ACM Trans. Graph., 14(3):203-232, 1995.

R. Davidson and D. Harel. Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics, 15(4):301-331, 1996.

P. Eades. A heuristic for graph drawing. Congressus Numerantium, 42:149-160, 1984.

Herodotus. The History of Herodotus. 440 B.C.

S. A. Hirsch. An algorithm for automatic name placement around point data. The American Cartographer, 9:5-17, 1982.

E. Imhof. Die Anordnung der Namen in der Karte. International Yearbook of Cartography, 2:93-129, 1962.

S. Kirkpatrick, Jr. C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671-680, 1983.

G. W. Klau, N. Lesh, J. Marks, M. Mitzenmacher, and G. T. Schafer. The HuGS platform: A toolkit for interactive optimization. In Proc. of AVI 2002 (International Working Conference on Advanced Visual Interface), 2002.

G. W. Klau and P. Mutzel. Optimal labelling of point features in rectangular labelling models. Mathematical Programming, 94(2-3):435-458, 2003.

J. Kruskal and J. Seery. Designing network diagrams. First General Conf. on Social Graphics, pages 22-50, 1980.

J. Marks and S. Shieber. The computational complexity of cartographic label placement. Technical Report TR-05-91, Harvard University, Cambridge, MA, U.S.A., 1991.

T. Strijk and M. van Kreveld. Practical extensions of point labelling in the slider model. In Proc. 7th ACM Symp. Adv. Geogr. Inform. Syst., pages 47-52, 1999.

M. van Kreveld, T. Strijk, and A. Wolff. Point labeling with sliding labels. Computational Geometry: Theory and Applications, 13:21-47, 1999.

P. Yoeli. The logic of automated map lettering. The Cartographic Journal, 9:99-108, 1972.