General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Cutting planes in integer and mixed integer programming
Discrete Applied Mathematics
A simplex-based algorithm for 0-1 mixed integer programming
Combinatorial optimization - Eureka, you shrink!
A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem
INFORMS Journal on Computing
Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs
Mathematics of Operations Research
Basis reduction and the complexity of branch-and-bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Theoretical Computer Science
Simple lifted cover inequalities and hard knapsack problems
Discrete Optimization
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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.