Labeling points with rectangles of various shapes

Atsushi Koike, Shin Ichi Nakano, Takao Nishizeki, Takeshi Tokuyama, Shuhei Watanabe

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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 languageEnglish
Pages (from-to)511-528
Number of pages18
JournalInternational Journal of Computational Geometry and Applications
Issue number6
Publication statusPublished - 2002 Dec


  • Geographic information systems
  • Map labelling
  • Parametric search
  • Plane sweep algorithm


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