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.
|Number of pages||9|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|Publication status||Published - 2001 Jan 1|
|Event||33rd Annual ACM Symposium on Theory of Computing - Creta, Greece|
Duration: 2001 Jul 6 → 2001 Jul 8
ASJC Scopus subject areas