### Abstract

Given a combinatorial problem on a set of weighted elements if we change the weight using a parameter we obtain a parametric version of the problem which is often used as a tool for solving mathematical programming problems. One interesting question is how to describe and analyze the trajectory of the solution. If we consider the trajectory of each weight function as a curve in a plane we have a set of curves from the problem instance. The curves induces a cell complex called an arrangement which is a popular research target in computational geometry. Especially for the parametric version of the problem of computing the minimum weight base of a matroid or polymatroid the trajectory of the solution becomes a subcomplex in an arrangement. We introduce the interaction between the two research areas combinatorial optimization and computational geometry through this bridge.

Original language | English |
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Pages (from-to) | 362-371 |

Number of pages | 10 |

Journal | IEICE Transactions on Information and Systems |

Volume | E83-D |

Issue number | 3 |

Publication status | Published - 2000 Jan 1 |

### Keywords

- Combinatorics
- Computational geometry
- Matroids
- Parametric optimization

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

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## Cite this

*IEICE Transactions on Information and Systems*,

*E83-D*(3), 362-371.