Minimax parametric optimization problems and multi-dimensional parametric searching

Takeshi Tokuyama

Research output: Contribution to journalConference article

10 Citations (Scopus)

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) Parame tric polymatroid optimization, for example, O(n log n) time algorithm to compute the parameter vector minimizing k-largest linear parametric elements with d dimensions.

Original languageEnglish
Pages (from-to)75-83
Number of pages9
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
Publication statusPublished - 2001 Jan 1
Event33rd Annual ACM Symposium on Theory of Computing - Creta, Greece
Duration: 2001 Jul 62001 Jul 8

ASJC Scopus subject areas

  • Software

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