## Abstract

Let S be a set of n points in the plane. We study the following problem: Partition S by a line into two subsets S_{a} and S_{b} such that max{f(S_{a}), f(S_{b})} is minimal, where f is any monotone function defined over 2^{s}. We first present a solution to the case where the points in S are the vertices of a convex polygon and apply it to some common cases - f(S′) is the perimeter, area, or width of the convex hull of S′ ⊆ S - to obtain linear solutions (or O(n log n) solutions if the convex hull of S is not given) to the corresponding problems. This solution is based on an efficient procedure for finding a minimal entry in matrices of some special type, which we believe is of independent interest. For the general case we present a linear space solution which is in some sense output sensitive. It yields solutions to the perimeter and area cases that are never slower and often faster than the best previous solutions.

Original language | English |
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Pages (from-to) | 39-51 |

Number of pages | 13 |

Journal | International Journal of Computational Geometry and Applications |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1999 |

## Keywords

- Bipartition
- Convex hull
- Geometric optimization

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics