Parametric polymatroid optimization and its geometric applications

Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)429-443
Number of pages15
JournalInternational Journal of Computational Geometry and Applications
Issue number5
Publication statusPublished - 2002 Oct


  • Combinatorial geometry
  • K-level
  • Matroid

ASJC Scopus subject areas

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


Dive into the research topics of 'Parametric polymatroid optimization and its geometric applications'. Together they form a unique fingerprint.

Cite this