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Lifted Cover Inequalities for 0-1 Integer Programs: Complexity

We investigate several complexity issues related to branchand-cut algorithms for 0-1 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 0-1 knapsack instances for which any branch-and-cut algorithm based on LCIs has to evaluate an exponential number of nodes to prove optimality.