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research article

Testing additive integrality gaps

Eisenbrand, Friedrich  
•
Haehnle, Nicolai  
•
Palvolgyi, Doemoetoer
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2013
Mathematical Programming

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.

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10107_2012_Article_518.pdf

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http://purl.org/coar/version/c_970fb48d4fbd8a85

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