### Abstract

Let S be a set of m convex polygons in the plane with a total number of n vertices. Each polygon has a positive weight. This paper presents algorithms to solve the weighted minmax approximation and the weighted minsum approximation problems. For the first problem, a line minimizing the maximum weighted distance to the polygons can be found in O(n^{2} log n) time and O(n^{2}) space. The time and space complexities can be reduced to O(n log n) and O(n), respectively, when the weights are equal. For the second problem, a line minimizing the sum of the weighted distances to the polygons can be found in O(n^{2} log n) time and O(n) space. For both problems, we also obtain similar results for sets of n circles or line segments.

Original language | English (US) |
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Title of host publication | STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings |

Editors | Alain Finkel, Matthias Jantzen |

Publisher | Springer Verlag |

Pages | 233-244 |

Number of pages | 12 |

ISBN (Print) | 9783540552109 |

DOIs | |

State | Published - 1992 |

Event | 9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992 - Cachan, France Duration: Feb 13 1992 → Feb 15 1992 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 577 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992 |
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Country | France |

City | Cachan |

Period | 2/13/92 → 2/15/92 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings*(pp. 233-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 577 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55210-3_187