Approximating integer programs with positive right-hand sides

Authors:
Peter Jonsson;Johan Thapper
Affiliations:
Department of Computer and Information Science, Linköpings universitet, SE-581 83 Linköping, Sweden;École polytechnique, Laboratoire d'informatique (LIX), 91128 Palaiseau Cedex, France
Venue:
Information Processing Letters
Year:
2010

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Abstract

We study minimisation of integer linear programs with positive right-hand sides. We show that such programs can be approximated within the maximum absolute row sum of the constraint matrix A whenever the variables are allowed to take values in N. This result is optimal under the unique games conjecture. When the variables are restricted to bounded domains, we show that finding a feasible solution is NP-hard in almost all cases.