Testing additive integrality gaps

We consider the problem of testing whether the maximum additive integrality gap of a family of integer programs in standard form is bounded by a given constant. This can be viewed as a generalization of the integer rounding property, which can be tested in polynomial time if the number of constraints is fixed. It turns out that this generalization is NP-hard even if the number of constraints is fixed. However, if, in addition, the objective is the all-one vector, then one can test in polynomial time whether the additive gap is bounded by a constant.

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Friedrich Eisenbrand, Nicolai Hähnle, Dömötör Pálvölgyi, Gennady Shmonin
• Keywords: Additive Integrality Gap, Discrete Algorithms, Integer Rounding Property, Polynomial Time, SODA 2010