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Conference Paper

Point Containment in the Integer Hull of a Polyhedron

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Althaus,  Ernst
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Eisenbrand,  Friedrich
Discrete Optimization, MPI for Informatics, Max Planck Society;

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Funke,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Althaus, E., Eisenbrand, F., Funke, S., & Mehlhorn, K. (2004). Point Containment in the Integer Hull of a Polyhedron. In Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04) (pp. 929-933). New York, NY: ACM.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2BA9-D
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 $\varphi$ bits can be solved in time $O(m+\varphi)$ in the two-dimensional case and in expected time $O(m+\varphi^2 \log m)$ 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.