Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
 
Minimax Parametric Optimization Problems and Multidimensional Parametric Searching
Takeshi TOKUYAMA
Author information
JOURNAL FREE ACCESS

2005 Volume 11 Issue 1 Pages 1-9

Details
Abstract

The parametric minimax problem, which finds the parameter value minimizing the weight of a solution of a combinatorial maximization problem, is a fundamental problem in sensitivity analysis. Moreover, several problems in computational geometry can be formulated as parametric minimax problems. The parametric search paradigm gives an efficient sequential algorithm for a convex parametric minimax problem with one parameter if the original non-parametric problem has an efficient parallel algorithm. We consider the parametric minimax problem with d parameters for a constant d, and solve it by using multidimensional version of the parametric search paradigm. As a new feature, we give a feasible region in the parameter space in which the parameter vector must be located.
Typical results obtained as applications are: (1) Efficient solutions for some geometric problems, including theoretically efficient solutions for the minimum diameter bridging problem in d-dimensional space between convex polytopes. (2) Solutions for parametric polymatroid optimization problems, including an O(n log n) time algorithm to compute the parameter vector minimizing k-largest linear parametric elements with d dimensions.

Content from these authors
© 2005 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
https://creativecommons.org/licenses/by/4.0/
Next article
feedback
Top