Lifted Cover Inequalities for 0-1 Integer Programs: Complexity

@article{Gu1999LiftedCI,
  title={Lifted Cover Inequalities for 0-1 Integer Programs: Complexity},
  author={Zonghao Gu and George L. Nemhauser and Martin W. P. Savelsbergh},
  journal={INFORMS Journal on Computing},
  year={1999},
  volume={11},
  pages={117-123}
}
We investigate several complexity issues related to branch and cut algorithms for integer programming based on lifted cover inequalities LCIs We show that given a fractional point determining a violated LCI over all minimal covers is NP hard The main result is that there exists a class of knapsack instances for which any branch and cut algorithm based on LCIs has to evaluate an exponential number of nodes to prove optimality 

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