Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Strongly polynomial-time and NC algorithms for detecting cycles in dynamic graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Minimax geometric fitting of two corresponding sets of points
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Geometric lower bounds for parametric matroid optimization
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Matroid optimization and algorithms
Handbook of combinatorics (vol. 1)
Minimum cuts in near-linear time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Is there an algebraic proof for P ≠ NC? (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Handbook of discrete and computational geometry
Linear programming in low dimensions
Handbook of discrete and computational geometry
Parametric polymatroid optimization and its geometric applications
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Using separation algorithms in fixed dimension
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
On optimal bridges between two convex regions
Information Processing Letters
Efficient Algorithms for the Minimum Diameter Bridge Problem
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Efficient algorithms for the minimum diameter bridge problem
Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry
Minimizing the sum of the k largest functions in linear time
Information Processing Letters
Efficient Algorithms for the Minimum Diameter Bridge Problem
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Building bridges between convex regions
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Smoothing method for minimizing the sum of the r largest functions
Optimization Methods & Software
Algorithmic results for ordered median problems
Operations Research Letters
| Hi-index | 0.00 |
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) Parametric polymatroid optimization, for example, O(n log n) time algorithm to compute the parameter vector minimizing k-largest linear parametric elements with d dimensions.