### 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) log^{2}(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 |
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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

*International Journal of Computational Geometry and Applications*,

*12*(6), 511-528. https://doi.org/10.1142/S0218195902001018