Combinatorics on arrangements and parametric matroids: A bridge between computational geometry and combinatorial optimization

Takeshi Tokuyama

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)362-371
Number of pages10
JournalIEICE Transactions on Information and Systems
VolumeE83-D
Issue number3
Publication statusPublished - 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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