Mathematical Programming

, Volume 141, Issue 1–2, pp 257–271 | Cite as

Testing additive integrality gaps

  • Friedrich EisenbrandEmail author
  • Nicolai Hähnle
  • Dömötör Pálvölgyi
  • Gennady Shmonin
Full Length Paper Series A


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.

Mathematics Subject Classification (2000)

90C10 52C07 11H06 68Q25 


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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  • Friedrich Eisenbrand
    • 1
    Email author
  • Nicolai Hähnle
    • 1
  • Dömötör Pálvölgyi
    • 2
  • Gennady Shmonin
    • 1
  1. 1.DISOPT, Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Eötvös UniversityBudapestHungary

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