On two intersecting set systems and k-continuous boolean functions
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
On the Chvátal rank of polytopes in the 0/1 cube
Discrete Applied Mathematics
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?
Mathematics of Operations Research
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
An Exponential Lower Bound on the Length of Some Classes of Branch-and-Cut Proofs
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Rank Bounds and Integrality Gaps for Cutting Planes Procedures
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Combinatorica
Approximate fixed-rank closures of covering problems
Mathematical Programming: Series A and B
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Integrality gaps of 2 - o(1) for Vertex Cover SDPs in the Lovész-Schrijver Hierarchy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Exponential lower bounds and integrality gaps for tree-like Lovász-Schrijver procedures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
SDP Integrality Gaps with Local ell_1-Embeddability
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
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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In this work, we study the strength of the Chvátal-Gomory cut generating procedure for several hard optimization problems. For hypergraph matching on k-uniform hypergraphs, we show that using Chvátal-Gomory cuts of low rank can reduce the integrality gap significantly even though Sherali-Adams relaxation has a large gap even after linear number of rounds. On the other hand, we show that for other problems such as k-CSP, unique label cover, maximum cut, and vertex cover, the integrality gap remains large even after adding all Chvátal-Gomory cuts of large rank.