Parametric polymatroid optimization and its geometric applications

Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

研究成果: Article査読

4 被引用数 (Scopus)

抄録

We give an optimal bound on the number of transitions of the minimum weight base of an integer valued parametric polymatroid. This generalizes and unifies Tamal Dey's O(k1/3n) upper bound on the number of k-sets (and the complexity of the k-level of a straight-line arrangement), David Eppstein's lower bound on the number of transitions of the minimum weight base of a parametric matroid, and also the Θ(kn) bound on the complexity of the at-most-k level (the union of i-levels for i = 1, 2,..., k) of a straight-line arrangement. As applications, we improve Welzl's upper bound on the sum of the complexities of multiple levels, and apply this bound to the number of different equal-sized-bucketings of a planar point set with parallel partition lines. We also consider an application to a special parametric transportation problem.

本文言語English
ページ(範囲)429-443
ページ数15
ジャーナルInternational Journal of Computational Geometry and Applications
12
5
DOI
出版ステータスPublished - 2002 10 1

ASJC Scopus subject areas

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

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