Point containment in the integer hull of a polyhedron

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 bits can be solved in time O(m + ) in the two-dimensional case and in expected time O(m + 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.

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Ernst Althaus, Friedrich Eisenbrand, Stefan Funke, Kurt Mehlhorn
• Keywords: Algorithms, Integer Hull, Point Containment Problem, SODA 2004, Two-dimensional Case