Abstract
The traditional map labeling problems are mostly \({\mathcal{NP}}\)-hard. Hence, effective heuristics and approximations have been developed in the past. Recently, efficient algorithms for the so-called boundary labeling model have been introduced which assumes that the labels are placed on the boundary of the map and connected by polygonal leaders to their corresponding sites. Internal labels have been forbidden. In this paper, we allow both. Since clearly internal labels should be preferred, we consider several maximization problems for the number of internal labels and we show that they can be obtained efficiently or in quasi-polynomial time.
The work is funded by the National Technical University of Athens research program ΠEBE 2008.
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
Bar-Yehuda, R., Rawitz, D.: Efficient algorithms for integer programs with two variables per constraint (extended abstract). Algorithmica 29(44), 595–609 (2001)
Bekos, M.A., Kaufmann, M., Nöllenburg, M., Symvonis, A.: Boundary Labeling with Octilinear Leaders. Algorithmica 57(3), 436–461 (2009)
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Multi-Stack Boundary Labeling Problems. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 81–92. Springer, Heidelberg (2006)
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Polygons Labelling of Minimum Leader Length. In: Kazuo, M., Kozo, S., Jiro, T. (eds.) Proc. 5th Asia Pacific Symposium on Information Visualisation (APVIS206). CRPIT, vol. 60, pp. 15–21. ACS Inc. (2006)
Bekos, M.A., Kaufmann, M., Symvonis, A., Wolff, A.: Boundary Labeling: Models and Efficient Algorithms for Rectangular Maps. Computational Geometry: Theory and Applications 36, 215–236 (2007)
Benkert, M., Haverkort, H., Kroll, M., Nöllenburg, M.: Algorithms for multi-criteria one-sided boundary labeling. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 243–254. Springer, Heidelberg (2008)
Cromley, R.G.: A spatial allocation analysis of the point annotation problem. In: Proc. 2nd International Symposium on Spatial Data Handling (SDH 1986), pp. 38–49 (1986)
Edelsbrunner, H.: Dynamic data structures for orthogonal intersection queries. Tech. Rep. F59, Tech. Univ. Graz, Institute für Informationsverarbeitung (1980)
Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th Annual ACM Symposium on Computational Geometry, pp. 281–288 (1991)
Fowler, R.J., Paterson, M., Tanimoto, S.L.: Optimal Packing and Covering in the Plane are NP-Complete. Information Processing Letters 12(3), 133–137 (1981)
Gusfield, D., Pitt, L.: A bounded approximation for the minimum cost 2-Sat problem. Algorithmica 8(2), 103–117 (1992)
Kao, H.-J., Lin, C.-C., Yen, H.-C.: Many-to-one boundary labeling. In: Hong, S.-H., Ma, K.-L. (eds.) Proc. 6th International Asia-Pacific Symposium on Visualization (APVIS 2007), pp. 65–72. IEEE, Los Alamitos (2007)
van Kreveld, M., Strijk, T., Wolff, A.: Point labeling with sliding labels. Computational Geomentry: Theory and Applications 13, 21–47 (1999)
Kucera, L., Mehlhorn, K., Preis, B., Schwarzenecker, E.: Exact algorithms for a geometric packing problem. In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 317–322. Springer, Heidelberg (1993)
Lin, C.-C.: Crossing-free many-to-one boundary labeling with hyperleaders. In: 3rd IEEE Pacific Visualization Symposium (PacificVis 2010), pp. 185–192. IEEE Press, Los Alamitos (2010)
Lin, C.-C., Wu, H.-Y., Yen, H.-C.: Boundary labeling in text annotation. In: 13th International Conference on Information Visualisation (IV2009), pp. 110–115. IEEE, Los Alamitos (2009)
Mehlhorn, K.: Data structures and algorithms 3: multi-dimensional searching and computational geometry. Springer-Verlag New York, Inc., Heidelberg (1984)
Poon, C.K., Zhu, B., Chin, F.: A polynomial time solution for labeling a rectilinear map. In: Proc. 13th Annual ACM Symposium on Comp. Geom (SoCG 1997), pp. 451–453 (1997)
Wolff, A., Strijk, T.: The Map-Labeling Bibliography, maintained since (1996), http://i11www.ira.uka.de/map-labeling/bibliography
Zoraster, S.: Integer programming applied to the map label placement problem. Cartographica 23(3), 16–27 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bekos, M.A., Kaufmann, M., Papadopoulos, D., Symvonis, A. (2011). Combining Traditional Map Labeling with Boundary Labeling. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-18381-2_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18380-5
Online ISBN: 978-3-642-18381-2
eBook Packages: Computer ScienceComputer Science (R0)