Discrete Applied Mathematics
Cutting Planes and the Parameter Cutwidth
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
Improving integrality gaps via Chvátal-Gomory rounding
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Design and verify: a new scheme for generating cutting-planes
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Lower bounds for lovász-schrijver systems and beyond follow from multiparty communication complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Intersection Cuts with Infinite Split Rank
Mathematics of Operations Research
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Lower bounds for the Chvátal-Gomory rank in the 0/1 cube
Operations Research Letters
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
0/1 polytopes with quadratic chvátal rank
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalities for the integer hull of a given polyhedron. The Chvátal rank of the polyhedron is the number of rounds needed to obtain all valid inequalities. It is well known that the Chvátal rank can be arbitrarily large, even if the polyhedron is bounded, if it is 2-dimensional, and if its integer hull is a 0/1-polytope.We show that the Chvátal rank of polyhedra featured in common relaxations of many combinatorial optimization problems is rather small; in fact, we prove that the rank of every polytope contained in the n-dimensional 0/1-cube is at most n2(1+log n). Moreover, we also demonstrate that the rank of any polytope in the 0/1-cube whose integer hull is defined by inequalities with constant coefficients is O(n).Finally, we provide a family of polytopes contained in the 0/1-cube whose Chvátal rank is at least (1 + ε) n, for some ε 0.