Point containment in the integer hull of a polyhedron

Authors:
Ernst Althaus;Friedrich Eisenbrand;Stefan Funke;Kurt Mehlhorn
Affiliations:
Max-Planck-Institute for Computer Science, Saarbrücken, Germany;Max-Planck-Institute for Computer Science, Saarbrücken, Germany;Max-Planck-Institute for Computer Science, Saarbrücken, Germany;Max-Planck-Institute for Computer Science, Saarbrücken, Germany
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

Citing 6
Cited 0

Theory of linear and integer programming

Theory of linear and integer programming
Triangulating a simple polygon in linear time

Discrete & Computational Geometry
Las Vegas algorithms for linear and integer programming when the dimension is small

Journal of the ACM (JACM)
Polynomial algorithms for multiprocessor scheduling with a small number of job lengths

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Computing Two-Dimensional Integer Hulls

SIAM Journal on Computing
A Polynomial Algorithm for Multiprocessor Scheduling with Two Job Lengths

Mathematics of Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that the point containment problem in the integer hull of a polyhedron, which is defined by m inequalities, with coefficients of at most &phis; bits can be solved in time O(m + &phis;) in the two-dimensional case and in expected time O(m + &phis;2 log m) in any fixed dimension. This improves on the algorithm which is based on the equivalence of separation and optimization in the general case and on a direct algorithm (SODA 97) for the two-dimensional case.