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Mixed Map Labeling

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Algorithms and Complexity (CIAC 2015)

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Abstract

Point feature map labeling is a geometric problem, in which a set of input points must be labeled with a set of disjoint rectangles (the bounding boxes of the label texts). Typically, labeling models either use internal labels, which must touch their feature point, or external (boundary) labels, which are placed on one of the four sides of the input points’ bounding box and which are connected to their feature points by crossing-free leader lines. In this paper we study polynomial-time algorithms for maximizing the number of internal labels in a mixed labeling model that combines internal and external labels. The model requires that all leaders are parallel to a given orientation \(\theta \in [0,2\pi )\), whose value influences the geometric properties and hence the running times of our algorithms.

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References

  1. Agarwal, P.K., van Kreveld, M., Suri, S.: Label placement by maximum independent set in rectangles. Comput. Geom. Theory Appl. 11(3–4), 209–218 (1998)

    Article  MATH  Google Scholar 

  2. Bekos, M., Kaufmann, M., Nöllenburg, M., Symvonis, A.: Boundary labeling with octilinear leaders. Algorithmica 57, 436–461 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bekos, M.A., Kaufmann, M., Papadopoulos, D., Symvonis, A.: Combining traditional map labeling with boundary labeling. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 111–122. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Bekos, M.A., Kaufmann, M., Symvonis, A.: Efficient labeling of collinear sites. J. Graph Algorithms Appl. 12(3), 357–380 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bekos, M.A., Kaufmann, M., Symvonis, A., Wolff, A.: Boundary labeling: Models and efficient algorithms for rectangular maps. Comput. Geom. Theory Appl. 36(3), 215–236 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Benkert, M., Haverkort, H., Kroll, M., Nöllenburg, M.: Algorithms for multi-criteria boundary labeling. J. Graph Algorithms and Appl. 13(3), 289–317 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chalermsook, P., Chuzhoy, J.: Maximum independent set of rectangles. In: Discrete Algorithms (SODA 2009), pp. 892–901 (2009)

    Google Scholar 

  8. de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 2nd edn. Springer-Verlag, Berlin, Germany (2000)

    Book  Google Scholar 

  9. Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Computational Geometry (SoCG 1991), pp. 281–288. ACM (1991)

    Google Scholar 

  10. Gemsa, A., Haunert, J.-H., Nöllenburg, M.: Boundary-labeling algorithms for panorama images. In: Advances in Geographic Information Systems (SIGSPATIAL GIS 2011), pp. 289–298. ACM (2011)

    Google Scholar 

  11. Huang, Z.-D., Poon, S.-H., Lin, C.-C.: Boundary labeling with flexible label positions. In: Pal, S.P., Sadakane, K. (eds.) WALCOM 2014. LNCS, vol. 8344, pp. 44–55. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  12. Imhof, E.: Positioning names on maps. The American Cartographer 2(2), 128–144 (1975)

    Article  Google Scholar 

  13. Kaufmann, M.: On map labeling with leaders. In: Albers, S., Alt, H., Näher, S. (eds.) Efficient Algorithms. LNCS, vol. 5760, pp. 290–304. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Kindermann, P., Niedermann, B., Rutter, I., Schaefer, M., Schulz, A., Wolff, A.: Two-sided boundary labeling with adjacent sides. In: Dehne, F., Solis-Oba, R., Sack, J.-R. (eds.) WADS 2013. LNCS, vol. 8037, pp. 463–474. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Klau, G.W., Mutzel, P.: Optimal labeling of point features in rectangular labeling models. Mathematical Programming 94(2), 435–458 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Löffler, M., Nöllenburg, M.: Shooting bricks with orthogonal laser beams: a first step towards internal/external map labeling. In: Canadian Conf. Computational Geometry (CCCG 2010), pp. 203–206. University of Manitoba (2010)

    Google Scholar 

  17. Löffler, M., Nöllenburg, M., Staals, F.: Mixed map labeling. CoRR, abs/1501.06813 (2015)

    Google Scholar 

  18. Marks, J., Shieber, S.: The computational complexity of cartographic label placement. Technical report, Harvard University (1991)

    Google Scholar 

  19. Mehlhorn, K., Näher, S.: Dynamic fractional cascading. Algorithmica 5(1–4), 215–241 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nöllenburg, M., Polishchuk, V., Sysikaski, M.: Dynamic one-sided boundary labeling. In: Advances in Geographic Information Systems (SIGSPATIAL GIS 2010), pp. 310–319, November 2010

    Google Scholar 

  21. Reimer, A., Rylov, M.: Point-feature lettering of high cartographic quality: a multi-criteria model with practical implementation. In: EuroCG 2014, Ein-Gedi, Israel (2014)

    Google Scholar 

  22. van Kreveld, M., Strijk, T., Wolff, A.: Point labeling with sliding labels. Comput. Geom. Theory Appl. 13(1), 21–47 (1999)

    Article  MATH  Google Scholar 

  23. Wolff, A., Strijk, T.: The map labeling bibliography. http://i11www.iti.kit.edu/map-labeling/bibliography/

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Correspondence to Frank Staals .

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Löffler, M., Nöllenburg, M., Staals, F. (2015). Mixed Map Labeling. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_25

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  • DOI: https://doi.org/10.1007/978-3-319-18173-8_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18172-1

  • Online ISBN: 978-3-319-18173-8

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