Abstract
In this paper, we consider the leader length minimization problem for boundary labelling, i.e. the problem of finding a legal leader-label placement, such that the total leader length is minimized. We present an O(n 2 log 3 n) algorithm assuming type-opo leaders (rectilinear lines with either zero or two bends) and labels of uniform size which can be attached to all four sides of rectangle R. Our algorithm supports fixed and sliding ports, i.e., the point where each leader is connected to the label (referred to as port) may be fixed or may slide along a label edge.
This work has partially been supported by the DFG grant Ka 512/8-3, by the German-Greek cooperation program GRC 01/048 and by the Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly the Program PYTHAGORAS (co-funded by the European Social Fund (75%) and National Resources (25%)).
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References
Agarwal, P., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Computational Geometry: Theory and Applications 11, 209–218 (1998)
Bekos, M., Kaufmann, M., Symvonis, A., Wolff, A.: Boundary labeling: Models and efficient algorithms for rectangular maps. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 49–59. Springer, Heidelberg (2005)
Chazelle, B., 36 co-authors : The computational geometry impact task force report. In: Chazelle, B., Goodman, J.E., Pollack, R. (eds.) Advances in Discrete and Computational Geometry, vol. 223, pp. 407–463. AMS (1999)
Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th ACM Symp. Comp. Geom (SoCG 1991), pp. 281–288 (1991)
Imhof, E.: Positioning Names on Maps. The American Cartographer 2, 128–144 (1975)
Iturriaga, C., Lubiw, A.: NP-hardness of some map labeling problems. Technical Report CS-97-18, University of Waterloo (1997)
Mehlhorn, K.: Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry. EATCS Monographs on Theoretical Computer Science, vol. 3. Springer, Heidelberg (1984)
Vaidya, P.M.: Geometry helps in matching. SIAM J. Comput. 18, 1201–1225 (1989)
Wolff, A., Strijk, T.: The Map-Labeling Bibliography (1996), http://i11www.ira.uka.de/map-labeling/bibliography/
Wagner, F.: Approximate map labeling is in Omega (n log n). Technical Report B 93-18, Fachbereich Mathematik und Informatik, Freie Universitat Berlin (1993)
Wagner, F., Wolff, A.: Map labeling heuristics: provably good and practically useful. In: Proceedings of the eleventh annual symposium on Computational geometry, pp. 109–118 (1995)
Yoeli, P.: The Logic of Automated Map Lettering. The Cartographic Journal 9, 99–108 (1972)
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Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A. (2005). Boundary Labelling of Optimal Total Leader Length. In: Bozanis, P., Houstis, E.N. (eds) Advances in Informatics. PCI 2005. Lecture Notes in Computer Science, vol 3746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11573036_8
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DOI: https://doi.org/10.1007/11573036_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29673-7
Online ISBN: 978-3-540-32091-3
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