PARAMETRIC POLYMATROID OPTIMIZATION AND ITS GEOMETRIC APPLICATIONS-Reference-Cited by-同舟云学术

PARAMETRIC POLYMATROID OPTIMIZATION AND ITS GEOMETRIC APPLICATIONS

Published:2002-10 Issue:05 Volume:12 Page:429-443
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

KATOH NAOKI¹,TAMAKI HISAO²,TOKUYAMA TAKESHI³

Affiliation:

1. Department of Architecture, Kyoto University, Yoshida-Honmachi, Sakyou-ku, Kyoto, 606-01, Japan

2. Department of Computer Science, Faculty of Science and Engineering, Meiji University, Kawasaki, Kanagawa, 214, Japan

3. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8577, Japan

Abstract

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(k1/3 n) 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

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

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195902000967

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