Abstract
We deal with a map-labeling problem, named LOFL (Left-part Ordered Flexible Labeling), to label a set of points in a plane in the presence of polygonal obstacles. The label for each point is selected from a set of rectangles with various shapes satisfying the left-part ordered property, and is placed near to the point after scaled by a scaling factor σ which is common to all points. In this paper, we give an optimal O((n + m) log(n + m)) algorithm to decide the feasibility of LOFL for a fixed scaling factor σ, and an O((n + m) log2(n + m)) time algorithm to find the largest feasible scaling factor σ, where n is the number of points and m is the total number of edges of the polygonal obstacles.
| Original language | English |
|---|---|
| Pages (from-to) | 511-528 |
| Number of pages | 18 |
| Journal | International Journal of Computational Geometry and Applications |
| Volume | 12 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2002 Dec 1 |
Keywords
- Geographic information systems
- Map labelling
- Parametric search
- Plane sweep algorithm
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
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Cite this
Koike, A., Nakano, S. I., Nishizeki, T., Tokuyama, T., & Watanabe, S. (2002). Labeling points with rectangles of various shapes. International Journal of Computational Geometry and Applications, 12(6), 511-528. https://doi.org/10.1142/S0218195902001018