The monotone circuit complexity of Boolean functions
Combinatorica
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
An exponential lower bound for the size of monotone real circuits
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research
Aggregation and Mixed Integer Rounding to Solve MIPs
Operations Research
Valid inequalities based on simple mixed-integer sets
Mathematical Programming: Series A and B
Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs
Mathematics of Operations Research
MIR closures of polyhedral sets
Mathematical Programming: Series A and B
Sequential pairing of mixed integer inequalities
Discrete Optimization
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We prove a monotone interpolation property for split cuts which, together with results from Pudlak (1997) [20], implies that cutting-plane proofs which use split cuts (or, equivalently, mixed-integer rounding cuts or Gomory mixed-integer cuts) have exponential length in the worst case.