Abstract
The boundary labeling problem was recently introduced in [5] as a response to the problem of labeling dense point sets with large labels. In boundary labeling, we are given a rectangle R which encloses a set of n sites. Each site is associated with an axis-parallel rectangular label. The main task is to place the labels in distinct positions on the boundary of R, so that they do not overlap, and to connect each site with its corresponding label by non-intersecting polygonal lines, so called leaders. Such a label placement is referred to as legal label placement.
In this paper, we study boundary labeling problems along a new line of research. We seek to obtain labelings with labels arranged on more than one stacks placed at the same side of R. We refer to problems of this type as multi-stack boundary labeling problems.
We present algorithms for maximizing the uniform label size for boundary labeling with two and three stacks of labels. The key component of our algorithms is a technique that combines the merging of lists and the bounding of the search space of the solution. We also present NP-hardness results for multi-stack boundary labeling problems with labels of variable height.
The work is co – funded by the European Social Fund (75%) and National Resources (25%) – Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly the Program PYTHAGORAS.
This is a preview of subscription content, log in via an institution to check access.
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
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Boundary labelling of optimal total leader length. In: Bozanis, P., Houstis, E.N. (eds.) PCI 2005. LNCS, vol. 3746, pp. 80–89. Springer, Heidelberg (2005)
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Multi-stack boundary labeling problems, Technical report (2006), Available online: http://www.math.ntua.gr/aarg/
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A.: Polygon labelling of minimim leader length. In: Asia Pacific Symposium on Information Visualisation (APVIS 2006), CRPIT 60, pp. 15–21 (2006)
Bekos, M.A., Kaufmann, M., Symvonis, A., Wolff, A.: Boundary labeling: Models and efficient algorithms for rectangular maps. Computational Geometry: Theory and Applications, Available online: http://www.sciencedirect.com/
Bekos, M.A., 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)
Bekos, M.A., Symvonis, A.: Bler: A boundary labeller for technical drawings. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 503–504. Springer, Heidelberg (2006)
Eades, P., Lin, T., Lin, X.: Minimum size h-v drawings. In: Advanced Visual Interfaces (Proceedings of AVI 1992). World Scientific Series in Computer Science, vol. 36, pp. 386–394 (1992)
Formann, M., Wagner, F.: A packing problem with applications to lettering of maps. In: Proc. 7th Annuual ACM Symposium on Computational Geometry (SoCG 1991), pp. 281–288 (1991)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
SmartDraw-7. Product web site: http://www.smartdraw.com
Stockmeyer, L.: Optimal orientations of cells in slicing floorplan designs. Information and Control 57(2-3), 91–101 (1983)
Wolff, A., Strijk, T.: The Map-Labeling Bibliography (1996), http://i11www.ira.uka.de/map-labeling/bibliography
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bekos, M.A., Kaufmann, M., Potika, K., Symvonis, A. (2006). Multi-stack Boundary Labeling Problems. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_10
Download citation
DOI: https://doi.org/10.1007/11944836_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49994-7
Online ISBN: 978-3-540-49995-4
eBook Packages: Computer ScienceComputer Science (R0)